They stand between two enormous burial mounds, in front of a small whitewashed church, in a village that gives no other sign of having once been the centre of a kingdom. The smaller stone came first. King Gorm the Old raised it for his wife: King Gormr made these monuments in memory of Thyrve, his wife, Denmark's salvation. Denmark's salvation is a striking thing to carve about a person, and it is the earlier of the two appearances of the country's name on these stones. In 1994 UNESCO inscribed the stones together with the mounds and the church on the World Heritage List, calling the ensemble an unparalleled example of both pagan and Christian Nordic culture.

Gorm's son answered his father's stone with something far larger, and far more political. King Haraldr ordered these monuments made in memory of Gormr, his father, and in memory of Thyrve, his mother; that Haraldr who won for himself all of Denmark and Norway and made the Danes Christian. Three sides carry the message. One holds the inscription. One shows a serpent coiled around a great beast, read as an image of the territory Harald had taken. The third shows Christ, arms out, standing in the shape of a cross and tangled in what look like branches - a crucifixion composed so that anyone raised on the story of Odin hanging from the world tree would recognise the shape of it. Harald was not asking his subjects to abandon their imagery. He was reusing it.

In the 1930s the art historian Rudolf Broby-Johansen gave the large stone the name that stuck: Danmarks dabsattest, Denmark's baptismal certificate. Both stones carry the country's name - tanmaurk in the accusative on Harald's, tanmarkar in the genitive on Gorm's - and the pair are bound up with the idea of Denmark as a nation rather than a collection of holdings. That identification runs deep enough to be printed: a facsimile of the Christ figure appears inside the front cover of Danish passports. A copy of the large stone stands in Rouen, in Normandy, near the Saint-Ouen Abbey Church, given by Denmark in 1911 for the millennium of Normandy.

The grey we see is not what Harald commissioned. Specks of pigment survive in the carved surfaces, enough to show that the runes and the figures were originally picked out in strong colour, and a plaster cast made in 1955 for the Danish Church in London was painted accordingly - reds, blues, yellows filling the cut lines, the great beast and the Christ figure leaping off the rock. Seen that way the monument stops looking like an antiquity and starts looking like what it was: new work, freshly finished, sited where every traveller through the district would have to walk past it.

A thousand years outdoors took a toll. When UNESCO specialists inspected the stones on 15 November 2008 they found cracks opening and recommended moving them indoors or protecting them where they stood. Then, in February 2011, someone sprayed the word GELWANE in green paint across both faces of the large stone, and across a nearby gravestone and the church door as well. Scholars spent weeks hunting for a meaning. There was none; the vandal turned out to be a fifteen-year-old boy and the word was invented. The paint had not fully hardened and the stones were cleaned. Denmark's Heritage Agency then decided to leave them in place and ran a competition for a shelter, choosing Nobel Architects from 157 entries. The stones now sit inside rectangular glass cases braced by solid bronze sides on a steel skeleton, climate-controlled to a fixed temperature and humidity. The anti-reflective coating on the glass casts a faint green tint, and the bronze weathers towards the same colour, which sets off the grey and reddish tones of the granite rather well.