The Roman Catholic Church has a process -- to its credit, not a completely ridiculous one -- by which it certifies some healings there as miraculous. Although the process isn't completely ridiculous, it's far from obviously bulletproof; the main requirement is that a bunch of Roman Catholic doctors declare that the alleged cure is inexplicable according to current medical knowledge.

I went to medical school in Ireland and briefly rotated under a neurologist there. One time he received a very nice letter from the Catholic Church, saying that one of his patients had gotten much better after praying to a certain holy figure, and the Church was trying to canonize (or beatify, or whatever) the figure, so if the doctor could just certify that the patient's recovery was medically impossible, that would be really helpful and make everyone very happy.

The neurologist wrote back that the patient had multiple sclerosis, a disease which remits for long periods on its own all the time and so there was nothing medically impossible about the incident at all.

I have only vague memories of this, but I think the Church kept pushing it, asking whether maybe it was at least a little medically impossible, because they really wanted to saint this guy.

(the neurologist was an atheist and gleefully refused as colorfully as he could)

This left me less confident in accounts of medical miracles.