The Sudarium of Oviedo is a bloodstained linen cloth kept by the cathedral chapter of San Salvador in Oviedo and venerated as the face cloth laid over Jesus after the crucifixion. Unlike the Shroud of Turin it carries no image, and the case made for it has always rested on the stains and on a documentary history claimed to run back to the seventh century.
Radiocarbon assay of sampled fibres returned a date in the region of the seventh century AD. Taken at face value that is a straightforward result and it is centuries too late for the tradition. The laboratory did not leave it at face value. It entered a caveat with the number: the cloth had absorbed oils across a very long history of handling and public veneration, and organic contamination of that kind can shift a measured radiocarbon age, because the assay dates the carbon in the sample rather than the object the sample came from.
That caveat is the whole difficulty. Contamination by younger carbon pulls a date forward, so a genuinely older cloth could in principle measure younger, and nobody has established how much younger this particular contamination is capable of making it. The direction of the possible error is known. The size is not.
The result was therefore published as a measurement rather than as a determination, and no repeat assay on a decontaminated sample has appeared since to close the gap.