The kings of France (and of Navarre) had allegedly the power of miraculously curing scrofula by touch. In the Middle Ages it become progressively a part of the coronation ceremony; the ritual words pronounced by the king were “Le roi te touche, Dieu te guérit”, the king touches, God cures, clarifying that the monarch was only the vehicle, and that God, by allowing the miracle to happen, was endorsing the new king as the rightful leader of France.
When Henri IV, a Protestant recently converted to Catholicism, was crowned, he had to overcome the political opponents that weren’t willing to accept him on the throne, and that were using his religious background as propaganda against him. That’s why Henri took special care to cure scrofula ostentatiously and have this event published by way of images and portraits sold in the kingdom (on which he was labelled as “Very Christian King”); as the miracle took place, in front of a large number of witnesses, it was a sufficient proof for the people of France of his truthful conversion to Catholicism, and that he was a legitimate king, not an undercover heretic.
This is the only case I know of a miracle independently confirmed by skeptic or hostile witnesses, which, in other words, seems to be a historical case of placebo-induced healing.