During the interval at an Istanbul Music Festival concert in Aya Irini, I waylaid my guests before they could head to the concession stand and led them instead through the darkened aisles to the west doors, where we peeked through a crack into the courtyard. They gasped in appreciation.

Still lustrous in the half-light of evening stood a huge porphyry sarcophagus, about the size of an SUV. Several scholars have suggested that this particular sarcophagus, all but forgotten in its present location, belonged to Constantine the Great and was created in the early fourth century, at the time of the foundation of the city that bore his name. Along with several other imperial sarcophagi now in the Archaeological Museum, it was brought into the Topkapı Palace by Mehmet the Conqueror to form a part of his collection of antiquities.

The city is full of such surprises. In fact, the experience at Aya Irini is emblematic of how Byzantine Constantinople may be experienced today: dimly, unexpectedly, out of context, often no more than a provocative glimpse through the cracks of the Ottoman and modern-day cities. But if you look for it Byzantium is still here, often just below the surface. Ask any building contractor: they hate working in the historic peninsula because they are certain to hit the Byzantine stratum when they dig new foundations. Ask any carpet-dealer in Sultanahmet: if you are lucky, he will take you through a back door and down a dark stairway into his personal portion of the substructures of the Great Palace of the Byzantine emperors. Even the Great Palace Mosaic Museum is so cleverly tucked away beneath the Arasta Bazaar that most shoppers miss it completely. And cavernous vaulted cisterns are encountered in the most unexpected places, now functioning as shopping malls, teahouses, carpentry shops and restaurants. One of my favourites is in Gülhane Park and is now an aquarium.

But not all Byzantium is buried: in addition to its twenty-odd surviving churches and sundry ruined palaces and fortifications, if you look around any grand imperial mosque, you will inevitably find columns, capitals and other marbles borrowed from its Byzantine predecessor. The Topkapı Palace is full of Byzantine marbles as well, and also preserves a handful of Byzantine relics in its treasury (not to mention more than forty Byzantine cisterns in its grounds). The process of spoliation and display continues: it is becoming increasingly popular for upscale hotels to have their own archaeological site or collection of artefacts. The Eresin Crown Hotel in Sultanahmet, for example, is built on an excavation site and exhibits more than forty marble fragments, a cistern, a fortification wall and a floor mosaic in its lobby. Have a drink at its Column Bar and ponder past glory.

Another recent trend shows promise: Sultanahmet hotels and restaurants are adopting Byzantine place names, even if some are topographically suspect. Do the owners of the Kathisma Restaurant actually know where the Kathisma once stood? I wish I did.

Throughout it all, Justinian’s Great church, the Ayasofya, endures as a point of reference and a constant reminder the glory of Byzantium. So prominent up close, it offers its own tantalising glimpses around town. As you walk through historic Galata, for example, the street will suddenly fall away, the buildings will part, and Ayasofya will materialise, framed by the streetscape. Once, after several hours at the Emniyet Müdürlüğü (police headquarters) arranging a residence permit, I emerged to find the welcoming vision of Ayasofya at its doorstep. Sometimes the fleeting impression of its silhouette will appear in the rear-view mirror of the taxi as it rounds a corner – or through the window of the Bosphorus ferry as it turns to dock at Eminönü. On my first visit to Istanbul, decades ago, I was trapped in a crowded bus during rush hour on an exceptionally hot day. As we inched across the Galata Bridge, out of the window I was confronted with a breathtaking view of Ayasofya. The contrast between my miserable bus-bound situation and the passing panorama could not have been more dramatic.

Living in a city of grand vistas, I’ve come to appreciate these tantalising glimpses through the cracks into the past. Or, to put it another way, there are the macro- and the micro-views: for every evocative panorama, there are the equally redolent details to put it all into human perspective.

For example, although Ayasofya can be seen from just about everywhere at almost any time, it was designed to be experienced from the interior. Moreover, it is one of those places where the architectural statement is so grand, so overwhelming, that we can easily forget to notice the details. Follow the Brownian movements of any first-time visitors: they stumble around, mouths open, trying to grasp the enormity of its scale, to comprehend its ethereal spaciousness. With its emphatic centrality, Ayasofya offers them no direction. There is really no place to go. First they are drawn towards the middle, lured by the sheltering canopy of the great dome. Then, as if alarmed by its weightlessness, they retreat to the margins and the safety of the colonnades. And finally they creep back out through the door by which they entered, as if pushed by some metaphysical force, eventually finding solace at the souvenir stand, where picture postcards provide perspective.

They are not alone. Justinian’s court historian, Procopius, found the experience of the interior “altogether terrifying” because of its scale and the weightless impression of the vaulting. At least the scaffolding provides a sense of scale (think of it as a fifteen-storey skyscraper). But the details repay closer inspection, and not just the inevitable imperial mosaics (which are not to be missed). Next time you go, look for the following: the main doors of the narthex have bronze curtain-hooks in the shape of giant fingers, pointing heavenwards; many of the columns, column bases and marble revetments preserve cuttings for inset crosses, which once marked a sort of sacred itinerary for the faithful coming to venerate the building; the figures in the Deesis mosaic cast shadows, as if they are illuminated from the adjacent window – something that wasn’t seen in Western art until the time of Caravaggio.

For the monumentally challenged, the Kariye Camii (Church of the Chora) offers a more intimate view into the Byzantine city. The lush vegetation and enveloping hotels, cafés and tourist shops prevent a clear view of the exterior, which is as irregular and complex as Ayasofya is monumental. But wander into the garden at the back, where a dramatic flying buttress was added in the fourteenth century to brace the older church on unstable terrain.

Jostling with tour groups in the interior can spoil the intimacy, but in late afternoon the building empties. Most visitors crane their necks as they try to decipher the mosaics. It is easy to get lost in the details of the narrative and fail to notice how wonderfully it all fits together – how the mosaics suit their vaulted compartments, and how the spaces enclose and shelter you as you move through them. Complex as it is, this is a building with intellectual rigour, attributable to the input of its fourteenth-century founder, the poet and politician Theodore Metochites, whose turbaned portrait has become one of the signature icons of Byzantine civilisation.

Here are a few details to look for on your next visit. First, the Byzantines did not quarry marble after the seventh century. The marble revetments are made from sliced columns. Note the Rorschach-like repeat patterns in the naos, narrower on the sides, widening towards the centre. Second, Theodore Metochites became stinking rich as minister of the treasury, the man responsible for the collection of taxes. The unique mosaic of the Enrolment for Taxation is dominated by an enthroned Byzantine bureaucrat who resembles the donor – a veiled reference to Metochites, this may represent the greatest glorification of tax collection in the history of art.

And thirdly, the Kariye has the best-dressed saints in all Byzantium, attired in the silken finery of the imperial court. The saints in the outer narthex look like catwalk models at a Paris fashion show. St George, for example (just left of the entrance), displays the layered look, starting with a long blue tunic trimmed in gold and richly embroidered at the collar, cuffs and hem. Over this he sports a snappy short tunic, knotted at the shoulder and belted at the waist. His ensemble is completed with a red embroidered chlamys draped over his left shoulder, pinned with a gold fibula at the right – the ideal look for those special state occasions.

Of course there is more to see. One of the distressing trends in recent years is the narrowing of the Byzantine tourist circuit and the difficulty of gaining access to many of the monuments which have been made public. Aya Irini is open only as a concert hall; St John Studion is permanently closed, awaiting much-needed repairs; visits to the mosaic chapel at the Fethiye Camii and to the palace known as the Tekfur Sarayı require advance arrangements from the directorate at Ayasofya (so plan ahead). Even the stunning Byzantine galleries and the Istanbul through the Ages exhibition at the Archaeological Museum are rarely opened (again, plan ahead): this year they were eclipsed by the Troy galleries, now given greater exposure, thanks to the recent film.

Perhaps Constantinople needs an epic film of its own to restore it to monumental proportions. Think of it: Madonna as Theodora, Antonio Banderas as Justinian, Russell Crowe as Belisarius. If they need a technical adviser, I’m ready.