These pictures are strikingly powerful. All the same, it is impossible not to notice that a certain coarsening in painting took place over the course of the eighth century. The gradual transformation from the diaphanous figures of the seventh century to the stiffer and less lifelike ones in the Chapel of Theodotus provides some support for the view that at least part of the explanation for the stilted way later Byzantine artists painted is that they lacked the technical skills to produce naturalistic images.

The later pictures from the first half of the ninth century continue the evolution into the rigidly hieratic images that Vasari identified with the maniera greca. There are a number of biblical scenes, but as the painting gets less and less naturalistic, it is increasingly difficult to work out what they depict. The most impressive pictures from the later period are the lines of imposing saints surrounding a seated, and very regal, Christ. He has Greek saints standing on his right and Latin ones on his left.

Santa Maria Antiqua's frescos are unique: although they are badly damaged, and only part of what was painted has survived the 1,200 years that has elapsed since most of the church disappeared under falling rocks, there is nowhere else that preserves such a rich collection of paintings from the early middle ages. That period, with its obsession with eternity and its conviction that nothing happened without divine intervention, now seems much more remote than antiquity. Santa Maria Antiqua conveys the sheer strangeness of that world. Standing in front of its images, you get a sense of the time when invisible and magical powers dominated everything else.

The frescos are being restored with exemplary care and expertise by a team led by Werner Schmid. He has been working on the church and its art for more than a decade. Much of Dr Schmid's labour has been devoted to undoing the effects of the last century's restorations. For instance, it used to be thought that the best way to protect frescos was to detach them from the walls on which they were painted. But that can cause very serious damage. The 20th-century restorers also surrounded the frescos with cement — a procedure whose merits are now contested, but which, in this case, Dr Schmid believes was effective in preserving the paintings. "If they hadn't used it," he told me, "we would probably now have much less."

Santa Maria Antiqua's greatest tragedy, however, is that it has been closed for so long: it is almost 40 years since it was open to the public, and it is still closed now. When I visited, a single bad-tempered custodian with nothing to do tried to stop me entering, and then attempted to kick me out when he wanted to go to lunch. Fortunately, Dr Schmid was able to intervene. He is doing everything he can to ensure that one day it will be possible for anyone to visit Santa Maria Antiqua — as is Dr Giuseppi Moranti of the Soprintendenza Speciale per i Beni Archeologici di Roma, which has overall responsibility for the site. The plan is to open the church for guided visits by the end of 2013, although given the history of the project, it would not be surprising if there were further delays. But I cannot overstate what a wonderful experience visiting it is. And if you contact the Soprintendenza, they may let you in. Failing that, you could always try praying to St Quiricus for a miracle.