In the year 326 the mother of Constantine, Saint Helena, then about 80 years old, having journeyed to Jerusalem, undertook to rid the Holy Sepulchre of the mound of earth heaped upon and around it, and to destroy the pagan buildings that profaned its site. Some revelations which she had received gave her confidence that she would discover the Saviour’s Tomb and His Cross. The work was carried on diligently, with the co-operation of Saint Macarius, bishop of the city. The Jews had hidden the Cross in a ditch or well, and covered it over with stones, so that the faithful might not come and venerate it. Only a chosen few among the Jews knew the exact spot where it had been hidden, and one of them, named Judas, touched by Divine inspiration, pointed it out to the excavators, for which act he was highly praised by Saint Helena. Judas afterwards became a Christian saint, and is honored under the name of Cyriacus.
During the excavation three crosses were found, but because the titulus was detached from the Cross of Christ, there was no means of identifying it. Following an inspiration from on high, Macarius caused the three crosses to be carried, one after the other, to the bedside of a worthy woman who was at the point of death. The touch of the other two was of no avail; but on touching that upon which Christ had died the woman got suddenly well again. From a letter of Saint Paulinus to Severus inserted in the Breviary of Paris it would appear that Saint Helena. herself had sought by means of a miracle to discover which was the True Cross and that she caused a man already dead and buried to be carried to the spot, whereupon, by contact with the third cross, he came to life. From yet another tradition, related by Saint Ambrose, it would seem that the titulus, or inscription, had remained fastened to the Cross.
After the happy discovery, Saint Helena and Constantine erected a magnificent basilica over the Holy Sepulchre, and that is the reason why the church bore the name of Saint Constantinus. The precise spot of the finding was covered by the atrium of the basilica, and there the Cross was set up in an oratory, as appears in the restoration executed by de Vogüé. When this noble basilica had been destroyed by the infidels, Arculfus, in the seventh century, enumerated four buildings upon the Holy Places around Golgotha, and one of them was the “Church of the Invention” or “of the Finding”. This church was attributed by him and by topographers of later times to Constantine. The Frankish monks of Mount Olivet, writing to Leo III, style it Saint Constantinus. Perhaps the oratory built by Constantine suffered less at the hands of the Persians than the other buildings, and so could still retain the name and style of Martyrium Constantinianum. (See De Rossi, Bull. d’ arch. crist., 1865, 88.)
(Cf. Catholic Encyclopedia: Cross and Crucifix)