Matthew Hoffman gives a guided tour through the heavenly vaults of Venice
In late 1993, I realised that I could collect Air Miles simply by paying bills with my bank-issued credit card. But where should I fly to, when I finally succeeded in garnering thousands of miles (which, at pounds 20 per mile, would obviously be some time off)? Three years later, on a cold, misty winter afternoon, I peered through the unwashed glass of a motoscafo speeding through the Venetian lagoon. The campaniles of Venice were spread out to starboard like the skyscrapers of New York as seen from the New Jersey turnpike. It was midweek, rather than a weekend, and I had booked three nights at an inexpensive pension just off the Grand Canal near the Accademia art gallery.

There was a problem, though. What can you do in such a treasure house as Venice in only three days? Or, more precisely, what can you do without? For me, the answer was determined by a summer holiday spent in nearby Vicenza in 1995. On that occasion, I had spent about 10 days touring the Veneto (Venice's historic mainland dependency) seeing as many as I could of the buildings of Andrea Palladio, the 16th-century Vicentine architect. Now I decided to confine my sightseeing on this short trip to Palladio's two complete churches, San Giorgio Maggiore and Il Redentore - or at least to make them my first priority.

Of course, I had seen the exteriors of these churches before. Who hasn't? Anyone who has ever stood in front of the Doge's Palace, at the heart of tourist Venice, and looked across the lagoon, has noticed the classical portico of San Giorgio floating there, anchored to its little island. And, turning to the right, along the waterfront of the Giudecca, with a little more discernment you may have picked out, from the line of smaller buildings, the compact, domed profile of Palladio's votive church dedicated to the Redeemer, in thanksgiving for deliverance from the plague of 1575- 6. On this trip, however, I wouldn't merely gaze from afar.

Within an hour of getting to town, I had walked across the Dorsoduro from my hotel to the Zattere water-bus stop and caught a number 82 vaporetto to Redentore on the Giudecca; but it was already late afternoon, with sunset fast approaching. The church is lit by natural light and it was, to be frank, gloomy inside. It had a chaste magnificence but none of the delight of, say, one of Veronese's frescoed rooms in Palladio's Villa Maser. Of course, it was dedicated to a serious purpose; it's not a nobleman's pleasure palace. But somehow I had not allowed for the difference. It was too dark to stay long, and I left for dinner a little disappointed.

The next day, after a morning spent among the glories of Venetian arts and crafts in the Museo Correr, I set out with trepidation for San Giorgio Maggiore. This time, though, I was delighted. Il Redentore may be made for spiritual reflection; San Giorgio is designed for show. The wealthy Benedictine monks must have wanted a church to rival the newly rebuilt St Peter's in Rome, for what they commissioned from Palladio is a magnificent showcase of High Renaissance grandeur. This is more Roman empire than Roman Catholic. Take the deep, U-shaped choir behind the chancel. Above the carved stalls there is an alternating series of windows and niches for standing sculptures, each element separated by an order of Corinthian half-columns surmounted by pediments and linked by a wide, sculpted moulding. A broad, classical cornice crowns the whole ensemble. Though the niches contain what are no doubt meant to be saints, the overall effect is like something out of a Roman temple.

Back in the main nave, through the aisles, into the apsidal arms of the transepts and under the high dome, there is a thrilling sense of spatial ordering. Architectural historians write of the rhythmic use of the intervals between bays, and repetitions and variations of motifs, as though the members of a building were like notes of a composition. That analogy had always seemed strained to me, but Palladio's compressions of pilasters and of capitals, seemingly overlapping as they turn the corners from the nave to the crossing to the chancel, are surely music frozen in space.

The next day in Venice I devoted to other matters, but on my last morning I set out early - more from a sense of duty than desire - to take a last look at Il Redentore. The Giudecca Canal was shrouded in fog and the church loomed up before me as I approached it from the vaporetto stop. I plunged on inside and found myself alone but for a cleaning woman. The contrast in upkeep with San Giorgio was immediately apparent. The latter church is now looked after by the well-endowed Cini Foundation, and the stucco of the walls is smooth, the paintwork fresh. Il Redentore has peeling plaster and discoloured surfaces: the Franciscans seem to have remained as poor as their founder. All Palladio's buildings pay great attention to tonal values: they look ill when shabby, although they bounce back to life with a little repair work.

Still, the mild, diffuse early morning light was a great improvement on that of late afternoon, and as I lingered in the church, the fog burnt off and shafts of rosy light filtered through the plain glass thermal windows. I took a few photographs, and then decided to sketch a couple of bays in the nave. That made all the difference. A few scratchy pencil marks revealed to me the arrangement of small and large classical orders, and the subtle interplay that linked them. Il Redentore reveals its secrets much more reluctantly than San Giorgio, but it is worth the wait and the effort to penetrate them.

Much of the church is cordoned off and only the nave is open to the public. But the cleaner left one of the side-chapel gates open, and from the change in angle of vision there my understanding of the building gained a new dimension. A priest then emerged, and, with his permission, I was able to explore more of the church: to walk under the dome, into the apses, around the altar.

In the book I Quattro Libri dell' Architettura, Palladio echoes his ancient Roman predecessor Vitruvius in pointing out that each building must be appropriate to its purpose. "Temples in particular", Palladio tells us, "ought to be so made, that they might have so much beauty, that nothing more beautiful could be imagined, and so disposed in each of their parts, that those who enter there, may be astonished, and remain in a kind of ecstasy in admiring their grace and beauty."

I can attest that this ecstasy is available, in very different forms, to those who will take the time to experience it, at both of Palladio's great Venetian churches.