like any other artifact, a relic should be accompanied by its provenance, which tells where it came from, and the history of the object since it was made. that is how an antique is authenticated (or part of it). If somebody just told you what it was, and there is nothing to show it actually came from the saint and what its history has been up until now, no there is no proof and no way to authenticate it.
That is one reason why there is debate about the authenticity of the Shroud, for instance. For a greater part of its alleged history, there is no provenance, nothing to show where it was, who had it, how it changed hands under what circumstances. Unless you can trace an antique object back through history to the time of origin, the object is said to lack provenance. So in the case of such an object, one would have to rely on other tests–carbon dating, analysis of the materials, published reports of the existence of the object at various times and places etc.
