The Armenian Apostolic Church:
In the Armenian Church, Abgar is regarded to be a saint and his story continues to be told as tradition. The Church calendar honors “St. Abgar” in a worship service in December of every year and the name Abgar continues as an Armenian given name. It also is the root of the surname Abgarian (also spelled Abkarian, or Abcarian); from the family of Abgar.
The Roman Catholic Church:
Despite an absence of Biblical reference or historical evidence that a person given the name Veronica ever existed, canonization took place and now “St. Veronica” is celebrated on special church festival days. The whereabouts of the veil is obscure; it is said to be in the Vatican archives but other locations have been suggested. A great number of churches and schools are named in honor of Veronica and it is a popular given name.
The Shroud of Turin
The Shroud of Turin underwent radiocarbon testing in 1988 and the result of the test indicated the cloth was made during the Middle Ages approximately 1300 years after the death of Jesus. Unanswered questions remain, however, and the test result neither satisfied nor was accepted by people who believe the Shroud is, in fact, the actual cloth used to cover the body of Jesus. The tested portion, they believe, was from a section that was a restoration and not part of the original cloth. It has not been tested again.
This could be an interesting discussion.