When Constantina, daughter of Emperor Constantine, died in Bithynia in 354, her body was returned to be buried at an imperial a mausoleum on the Via Nomentana. The monumental red porphyry sarcophagus at the Pio Clementino Museum in the Vatican Museums comes from the mausoleum where she was buried on the Via Nomentana, which was later transformed into the Church of Santa Costanza. The mausoleum and the sarcophagus found there are generally believed to be her sarcophagus.

The relief decoration of sarcophagus shows cupids, amidst vine scrolls, gathering and pressing grapes - a Dionysiac subject often adopted by early Christians as a symbol of the Eucharist. The long sides have other subjects from the Dionysiac repertory: peacocks, rams, and cupids bearing garlands. Interestingly, a fragment of a porphyry sarcophagus once at the Church of the Holy Apostles is almost identical to this sarcophagus. The similarity between the two sarcophagi suggests they were contemporary and made in the same place, perhaps Egypt.

Between 1467 and 1471 the sarcophagus was removed to Piazza San Marco in Rome and later, in 1790, it was taken into the Vatican Museums on a cart dragged by 40 oxen. It rests on four lionesses supports which were carved by Francesco Antonio Franzoni.