EDITH TEMPLETON (1916-2006) was born and educated in Prague. She left, shortly before the full horrors of the Second World War burst upon Bohemia, to marry an Englishman. In 1954 she wrote The Surprise of Cremona, which Cyril Connolly dubbed "a striptease Baedeker". Soon afterwards, she went to live in India with a second husband, who was physician to the King of Nepal.

The book remains quite possibly the best description of Cremona, Parma, Mantua, Ravenna, Urbino, and Arezzo. As befits the author of the obscene publication Gordon (banned in Britain and Germany in 1966), it is very much an account of one woman's adventures in the old towns of north Italy. It breathes sentiment and pleasure, but is also sensitive and scholarly.

After a disastrous first night, in a room furnished incongruously with piano and whatnot in Urbino, the hometown of Raphael and of Federico Barocci, Mrs Templeton makes a foray to the Ducal Gallery. An overheard English woman's judgement, on the sweetness of a baby Jesus, sends her out; and her visit the next day with an assistant curator fares no better: he talks Raphael down, insisting rather on the value of Piero della Francesca, evidently much to her dislike.

So Mrs Templeton shrugs off the assistant owl as "one of those booksy boys who repeat what their predecessors have written down", and leaves the gallery without ever going to the upper floor, where the treasures of Federico Fiori, "Il Baroccio", as he is nicknamed after a two-wheeled ox-cart, are displayed.

Sadly, too many visitors to the Duke of Urbino's palace follow in her footsteps today, although, I hope, unwittingly and without all her artistic prejudices.

To understand Barocci, who was born and died in Urbino (1533?-1612), it is necessary to visit his birthplace. This substantial anniversary exhibition has come to London from St Louis, Missouri. It is not as comprehensive as the Siena winter show in 2009, but it revolves around seven major altarpieces, many being shown outside Italy for the first time; devotional paintings; and elaborate preparatory works. They delineate his importance as a Counter-Reformation artist and an influential colourist.

The exhibition is broadly chronological. It takes us from the 1566- 67 Crucifixion to the 1607-09 Aldobrandini Institution of the Eucharist, and brilliantly serves as a short-hand history of the lives of Jesus, leading us from The Nativity (The Prado) through The Last Supper (Urbino) to Calvary (also Urbino), and of his mother, in a cycle that includes The Visitation, the wonderfully interior Nativity, the Rest on the Return from Egypt beneath a cherry tree (this from the Vatican), and the strikingly Mannerist Immaculate Conception (1574-75). Parish groups who make this a part of their Easter devotion will deeply enrich their faith.

The show is lavishly accompanied by a wealth of preparatory materials for each work; more than 1500 drawings, pastels, and oil sketches survive, indicating how meticulous Barocci was, and how exacting his patrons were. We see him both as a pioneer, not least in the use of pastels that he made himself, and as a sublime compositor and a noted printmaker, as the exhibition at the Fitzwilliam Museum in Cambridge (Arts, 12 May 2006) adumbrated.

Throughout the Cinquecento, Barocci was regarded as the equal of Raphael and Michelangelo, of Titian and Correggio. His fame spread throughout Italy, Spain, Flanders, Bavaria, and Bohemia. His works were widely available, whether in shrines such as Loreto or the celebrated Kunstkammer of Prague. He is now not so widely regarded, and there may be some for whom this offers a first encounter.

One picture, the only secular painting the artist essayed (Aeneas Fleeing Troy), was painted in 1598 for the Emperor Rudolph II in Prague, but disappeared after being sold in an English saleroom in 1800. It would be tremendous if that ruined work surfaced again as a result of this show's including the second version, from ten years later (now in Rome), faithfully copied for Cardinal Borghese from an oil sketch that has been re-identified at Windsor Castle.

Barocci's brilliance as a religious painter lies in his effortless ability to excite the mind of the faithful, and to turn such emotional engagement into a proper devotion. True, his figures can appear too "sweet", and would no doubt have occasioned Mrs Templeton to sneer. But his formal use of colour excites the emotions of the viewer and imparts a sense of awe in the true worshipper.

Who else would risk making Jesus in the Upper Room look so fey while four angels circle above (Urbino, Metropolitan Basilica of the Assumption), or make him look so happily asleep in a hammock in the 1579-82 Entombment of Christ, which he painted for the Confra- ternity of the Blessed Sacrament in Senigallia?

But this Entombment, which develops ideas from Raphael's Bor-ghese painting of the same subject, also offers a profound meditation on the sleep of death. We sleep in death that we might rise in glory. Henry Vaughan was right after all: "Graves are beds now for the weary, Death a nap, to wake more merry."

The work was so widely copied that, according to Giovan Pietro Bellori, it was almost destroyed by the temerity of one over-enthusiastic artist who pierced the canvas at several points in tracing it, and the Duke was obliged to prevail upon Barocci to repaint it, which he did in 1587.

When Barocci was first approached in February 1578, he asked for 600 scudi, but later the commission was agreed at half that, when the contract was finally offered in July 1579. It took three years to paint. The outstanding oil modello for it was one of the highlights at Christie's in the scandalous sell-off from Chatsworth of drawings in July 1984, and has here been loaned by the Getty. Mary Magdalene kneels at one side, as if at a remove, prayerfully waiting by the tomb-mouth that presages her Easter-morning encounter with the gardener.

In 1963, the art-historian Wittkower speculated that Barocci was a dreadful old hypochondriac suffering from grief and fearful of dreams. It is a commonplace canard lobbed against the faithful, and many saints have been of a weak and failing disposition. It also overlooks what we know of this artist.

In 1560, Pius IV had summoned him back to Rome, where he had earlier worked (1548-52). When he left the Vatican in 1563, it was because he was fearful that his stomach ailments were the result of a rival's trying to poison him, and not of a want of good doctors. Four years later, when the symptoms eased, he claimed to have been healed by the intercession of the Virgin Mary. By 1566, he was already a Franciscan lay-confraternity member of the Capuchins, the reformed branch of the order.

His constitution may have been weak, but his paintings are lively accompaniments of a spiritual quest such as that which St Philip Neri advocated. The 17th-century writer Bellori stated in his Lives of the Modern Painters that, "Because of the fervour of their founder, St Filippo Neri, who desired that sacred images be painted by excellent artists, Barocci received the commission."

The first altarpiece for the Oratory church of the Chiesa Nuova, The Visitation of the Virgin to her Cousin Elizabeth (383 x 247cm), was commissioned in 1582, and finally delivered to Rome in 1586 to great éclat. Queues formed to view it, lining the street for three days after it was unveiled. Neri himself took to sitting in front of the altarpiece, lost in devout contemplation of the solemn encounter between two pious women who announce the salvation of the world with a manly handshake.

It is said that Neri became annoyed when he found that he had become something of a tourist attraction himself, exciting the ecstatic interest of admiring females who hid in the neighbouring chapel. Certainly, early witnesses to the process of Philip Neri's canonisation, which began almost as soon as he died in 1595, often reported "seeing" him in the chapel, still wrapt in prayer before Barocci's altarpiece. Exceptionally, the church has loaned it for this exhibition; we may no longer live in an Age of Faith, but maybe St Philip Neri will be sighted among the throngs in Trafalgar Square going to the gallery.

It is a work in which emotion and devotion are united, as Bellori recognised: "It is so rare to see pictures in churches that meet the requirements of decorum and holiness in order to stimulate devotion."

The second altarpiece for the Oratorians, The Presentation of the Virgin in the Temple - sadly, not in the show - was received with equally enthusiastic acclaim in 1603; it had taken ten years to complete.

Another Marian altarpiece, of the coronation of the Virgin, was planned for the south transept, but Barocci's slow working method (poor sight, evident in his humble self-portrait, restricted him to paint for a few hours a day) led to its being cancelled. Nevertheless, Barocci proposed that he provide the high altarpiece, a commission that finally fell to Rubens.

Although this never came to anything (for lack of funding), the pope made good, and in 1603 commissioned The Institution of the Eucharist, for his family's chapel in the church of S. Maria sopra Minerva, opposite the Pantheon, in Rome. Philip Neri had been the pope's confessor up until his own death, but Pope Clement VIII (1592-1605) did not live long enough to see the altarpiece installed, in 1609.

Barocci was more than sympathetic to the Oratorians, having come into their ambit through his friendship with the Cardinal Archbishop of Milan, Federico Borromeo (1564-1631), who was one of Philip Neri's disciples, and one of the great benefactors of the Oratory. There may also have been a family link, as Barocci's uncle had furnished Neri with a watch, while Barocci's first Roman patron and Cardinal Borromeo had the same doctor, who almost undoubtedly served Barocci when his stomach failed.

Both Borromeo and the Aldobrandini pope shared the new Christian optimism that Philip Neri had espoused, and which is reflected in Barocci's work. This had been encouraged by the victory at Lepanto over the Turks (1571), and by Philip II's 1585 decisive victory regaining Antwerp in the Spanish Netherlands. Even the failure of the armadas of 1588 and the following year did not dint this enthusiasm.

In writing of the artist's works, Bellori gives the longest entry for the Aldobrandini altarpiece. In that, he records how the pope kept himself closely informed of the progress of the picture. When he saw the Chatsworth sketch that is on show here, he insisted that the figure of Satan tempting Judas at table to betray his master be omitted, as the devil was too close to the Lord himself.

The Holy Year (1600) saw a new vigorous Church Triumphant emerge, but already the art of a sexagenarian from the Marches increasingly looked too soft. Despite that, his influence, especially as a colourist, remained for the next two centuries.

Besides the religious works, there are four staggering portraits. These come as no surprise after the marvel of the oil-sketched heads that we have already encountered such as those for Anchises (Windsor) and for the principal characters at the deposition.

The youthful intelligent Francisco Maria II della Rovere became Duke of Urbino in 1574, succeeding his father. He was a life-long friend of the artist, and in 1571 he was among the celebrated heroes of Lepanto. In the Uffizi portrait, he stands proudly confident in scintillating armour, one hand resting on his helmet in conscious homage to Titian's great portrayal of Philip II.

Sadly, the Duke of Northumberland has not let the London audience see the autograph copy from his collection which in St Louis stood proudly shoulder to shoulder with the Florentine original. Instead, we get to see the Italian Embassy's portrait of Federico Bonaventura (1602), spruced up for the occasion, which Barocci painted in the last year of the count's life. This portrait, more than any other, may help explain why the late art-historian John Shearman felt that Barocci was a greater artist on the whole than El Greco.

"Barocci: Brilliance and Grace" is at the National Gallery (Sainsbury Wing), Trafalgar Square, London WC2, until 19 May. Phone 020 7747 2885. www.nationalgallery.org.uk