I WENT to live in Italy in March 1974 to attend the University of Florence. As part of the excuse was to test a vocation to the religious life, I lodged in the daughter house of the Olivetan Benedictines of San Miniato al Monte.

I was given two pieces of unsolicited advice by a Frenchwoman who befriended me and took over my European education during the four-hour Channel crossing. She warned, "Never speak to the Carabinieri." In an Italy of Red Brigades and of police baton- charges, they did not often ask questions first.

Attitudes change, although the first time I risked talking to one of them was only ten years ago, when I found two Carabinieri officers, arm in arm; both men had ear piercings and seemed more interested in one another than in shooting me. Nowadays, it is the Carabinieri who spearhead the recovery of national treasures, looted and sold illegally, often to museums in the United States.

As a 17-year-old, I could not have known that, 40 years on, I would ever be taken into the élite police training college in the heart of Florence. The Carabinieri have long occupied the former conventual house next to the Church of Santa Maria Novella, where the popes traditionally retained a suite of rooms. Napoleon turned it into a military base in 1808, and it remains off-limits to the public.

Here, on the first floor of the Grand Cloister, is a papal chapel decorated in under a month in the autumn of 1515 for the visit of the Medici Pope Leo X on 30 November, two-and-a-half years after he had succeeded Pope Julius II.

Entering the city in triumph on the feast day of St Andrew, the papal cavalcade traversed the city from the Porta Romana. Contemporary accounts of the official entrata call to mind the Field of the Cloth of Gold (1520).

The city itself had been transformed to look like ancient Rome, with fake statuary and false façades painted by the likes of Andrea di Cosimo Feltrini (1477-1548), and the younger artists Ridolfo del Ghirlandaio and Jacopo Carucci, called Pontormo, after his native birthplace in Tuscany near Empoli. The same three artists had the responsibility for renovating the papal chapel.

Pope Leo did not stay long, as he moved in with his family elsewhere in the city, and then hastened to Bologna to meet the King of France, returning for Christmas. I suspect his homecoming took longer than mine; 27 minutes on a high-speed train, travelling in a tunnel between both cities at speeds of 250km per hour.

As I came to the vaulted chapel, with sounds off of someone practising the tuba, as officers and men set off to jog or go on command, it was Pontormo's startling Veronica that took my immediate attention. The kneeling saint sways in a serpentine motion. For all the world, she looks like an erotic dancer holding up the sacred veil as yet one more veil. This hooded sibyl-turned-Calvary- bystander is Diana, Princess of Wales, talking to Martin Bashir. It is a compositional device that seems to be learned from Michelangelo, but it is disquieting, as it projects both innocence and ambiguity.

At the time when it was painted, the Veronica was in the treasury of the Lateran Palace. Like so many other purported relics taken from Constantinople in 1204, or later offered by the Byzantines, this was lost in the Sack of Rome a dozen years later, when, in 1527, the Emperor's troops ran amok.

The double anniversary of the births of Pontormo and Giovanni Battista di Jacopo Rosso in 1494 was marked 15 years back by a run of exhibitions that viewed them as exponents of Mannerism, "the modern manner", as Vasari dubbed it in his 1550 Lives of the Italian Artists, published by Lorenzo Torrentino, a copy of which neatly concludes this present show.

Whereas Vasari lauded the deceased Rosso for taking the new style of art with him to the French court, he castigated Pontormo for his failing to follow Michelangelo more fully. That judgement has largely clouded views of both artists ever since, and, in Pontormo's case, led to his being out of fashion until the post-war years had opened Italy up once more to visitors.

Curated by the same team as the 2010-11 Bronzino extravaganza at the Strozzi (Arts, 7 January 2011), this outstanding show challenges the presumed links between both artists to argue that, while they are in one sense twins, they are certainly not identical.

It also wrestles seriously with hard theological questions in an era of reform and change. The citizens of Florence overthrew the ruling family of the Medici in 1494, and formed a republic in which the firebrand Dominican preacher Girolamo Savonarola seized moral authority, calling for a more puritanical way of life and rejecting the excesses of the Medici court. It was not until the 1517 Council of Florence that apocalyptic preaching was banned across the city, even though Savonarola had been burnt at the stake in 1498.

In 1511, Pope Julius II sent Cardinal Giovanni di Lorenzo de' Medici at the head of a papal army to overthrow Florence, which later caved in to a bloodless revolution; it was his return, as Pope Leo X, four years later, that marked the importance of the city as all but a personal fiefdom.

The exhibition begins in 1511 with both artists in the workshop of Andrea del Sarto, painting in a city under siege. Del Sarto had been commissioned to decorate the little cloister of the Servite church of the Annunziata, and brought along his apprentices. Their very distinct styles already surface in these early frescoes.

Rosso's 1513 Assumption and Pontormo's Visitation here face one another in the first room. New scholarship has established that Rosso also painted the single foreground figure in del Sarto's fresco of the Journey of the Magi. Swathed in a theatrical mauve and yellow, this overflowing figure takes us back to the Rome of Raphael and the licentiousness of a city that had so appalled Luther in 1510.

In 1516/17, Del Sarto painted an altarpiece for the nuns of San' Francesco de Macci which is nicknamed "the Madonna of the Harpies", as the painted locusts around the base of the classical altar from which the Virgin rises resemble these classical creatures. Its composition clearly informs the one that Pontormo provided the following year for the Pucci chapel in the church of San Michele in Visdomini, where it still hangs.

In this display, both are placed next to Rosso's less successful, and unfinished, altarpiece painted for the hospital of Santa Maria Nuova with the bequest of a wealthy Catalan widow (Uffizi). The Carthusian patron was less than happy with the loose painting style and the awkwardly elongated figures, and withheld some of the agreed fee.

In the 1520s, the altarpiece was found a home in the village of San Stefano a Grezzano, and two of the figures were reworked. St Leonard, the patron saint of prisoners and the namesake of the unhappy commissioner, lost his fetters and gained a stone to identify him as St Stephen, and, by the addition of a Tau cross on his cloak, St Benedict was transformed into Anthony of Egypt.

Success came for Pontormo when he was appointed in 1519 to decorate the Medici villa at Poggio a Caiano, and he remained working in and around Florence until his death on New Year's Eve 1556. In the same year, Rosso was seemingly forced to travel abroad, heading first to Naples and then back to Volterra in search of work.

Rosso ended up in Rome in 1524, where he was captured by the Duke of Bourbon's Landsknecht during the Sack of 1527, and then, after an unsettled period in Umbria, Tuscany, and Venice, he moved to the French court in 1530. He worked at Fontainebleau, was housed in Paris, and enjoyed the income of a canonry of the Sainte Chapelle, dying there in 1540.

There are some unfortunate gaps in the show. The Getty has not sent the great painting of Pontormo's Halberdier (1528-30), and someone in Volterra blocked the loan of Rosso's profoundly moving 1521 Deposition from the Cross. The Diocesan Museum there has, however, lent the po-faced Madonna and Child with Saints John the Baptist and Bartholomew painted in the same year.

Missing, too, are Pontormo's portraits of Alessandro Medici, from Lisbon and from Philadelphia; but this a mere quibble, given that we see all bar one of Rosso's portraits, that of a young man, painted around 1517 or 1518 (Berlin). Many of Rosso's sitters were members of the select company of the Accademia di Belle Arti, which was founded 450 years ago. At that date, it was an all-male foundation, and I was surprised to learn that its restricted membership now includes Gina Lollobrigida. She has been elected in her own right as a sculptress, and not as remembered from my schooldays.

Restored for this exhibition is Rosso's extraordinarily colourful depiction of The Marriage of the Virgin (1523), painted during his second Florentine period. The Ginori altarpiece from the basilica of San Lorenzo centres on the figure of the Aaronic priest who draws an Adonis-looking blonde youth towards the Virgin. He wears a mitre on which is prominently written TETTAGRAMATON (sic), to which the Dominican St Vincent Ferrer points deliberately.

This suggests a hermetic reading of the painting recalling the suppressed teachings of Savonarola. The prominent inclusion of St Apollonia - who, like him, was a noted orator burned at the stake - with an open book on her knee offers a further possible allusion.

The youth of St Joseph is more unusual, given the traditional (but non-biblical) supposition by artists that he was an older man. Debates about chastity discussed whatcould have been the benefit to Joseph if age rather than continence alone maintained the virginity of Mary.

Besides a wealth of paintings, a dozen of Pontormo's surviving 200 or more drawings feature, including, crucially, two studies for the Capponi chapel in the Church of Santa Felicita. This little church, nestling beneath the Vasari corridor that links the Palazzo Pitti to the Uffizi, is not to be missed, and is only a short walk across the Ponte Vecchio.

In the altarpiece of the Deposition, two boys bear the Body of Christ not to an earthly tomb, but down towards the altar, at which the faithful will be fed with the bread of angels. The Virgin reels backwards in a final leave-taking. The other related drawing is for the angel for the Annunciation.

Only some 50 of Rosso's drawings are thought to survive; so the selection of nine of them here is generous, and shows that he was the equal of Pontormo as a draughtsman. He was also adroit as a salesman and exploited the comparatively new technique of engraving to advertise his work.

The Palazzo Vecchio has a temporary display of the panels Pontormo painted for the processional wagon provided for the city's patronal celebrations by two of the guilds for the Mint in 1514. The wagon (in effect an impossibly tall tower festooned with pictures) led the civic dignitaries every year on 24 June from the Piazza della Signoria to the Baptistery in the festa that was abolished in 1808.

Among the little panels for the wagon, one represents The Visitation, which makes for a fascinating comparison with the most powerful painting in the Strozzi palace, which is the loan of the same scene from the village of Carmignano.

This almost mystical encounter includes reduplicated images of the Virgin and her kinswoman which have provoked all sorts of theological theories: not quite strangers, but having the effect of alienating us from the world in which two embrace in silence, watched as if from behind a mirror.

Bill Viola captured an element of this dimensionality in his 1995 video The Greeting (in the show), but muddled his sources, so that his painfully slow and beautiful scene unfolds as if three women have been caught shopping in a Tuscan street.

From their silent world out into the warm bustle of a lively city square is a journey of more than 500 years. And, you ask, the Frenchwoman's other piece of advice? "Never sleep with strangers."

"Pontormo and Rosso: Diverging Paths of Mannerism is at the Palazzo Strozzi, Piazza Strozzi, Florence, Italy, until 20 July. Phone 00 39 055 264 5155.www.palazzostrozzi.org