There is no more comprehensive work on the credibility of New Testament's account of miracles (e.g., Jesus'), than the two-volume monograph written by Craig Keener,
Miracles: The Credibility of the New Testament Accounts (Grand Rapids: Baker Academic, 2011).
Keener, of course, is a Protestant. Yet one of my favorite aspects of his book is his treatment of the miracles at Lourdes, the site where the Blessed Virgin Mary is said to have appeared (vol. 2, pp. 675-686).
Scholars have long turned to Lourdes as a stunning example of well-documented instances of miraculous healings. A great treatment can be found in John P. Meier's work. Meier writes that even though numerous cases have been certified by impartial medical examiners as inexplicable (1,300 between 1948 and 1993) only 18 have been recognized by the Catholic Church as legitimately “miraculous” (cf. Meier,
A Marginal Jew, 2:528, n. 528).
I won't reproduce the whole section but Keener has
numerous reports, including ones from non-Catholic sources (e.g., a Methodist source).
He concludes with the following:
Whether one feels free to count the religious context at Lourdes affects one's interpretation of the results. One scholar skeptical of supernatural approaches readily grants that the healings occur. He affirms that "some utterly extraordinary cures" have occurred there 1, noting that enemies of the Catholic Church and leading medical scientists like Alexis Carrel have been persuaded by the data.2 He concedes that some cases cannot even be explained psychosomatically;3 among examples, he lists "the instant healing of a terribly disfigured face, and the instantaneous healing of a club foot on a two and one half year old child," showed by non-Catholics to be permanent. Further, he cited a news article about a three-year old with terminal cancer and the bones being eaten away; after the healing, even "the bones in her skull grew back. Her doctor, a Protestant, said that 'miracle' would not be too strong a word to use."4
Yet this same scholar notes that scientists can reject the supernatural interpretation at Lourdes by suggesting that some sort of naturalistic interpretation would arise if only we had sufficient evidence. The collocation of natural factors in this case might occur together only one in ten million times, he argues, but, because he assumes the miraculous impossible, must have occurred here.5 Scientists need autonomy to do their work, he insists, not having to wait to see if theologians will pronounce some event miraculous.6 Some theologians might wish to retort that they need some autonomy to evaluate miracles without the theological premise of their entire discipline being ruled out by thinkers committed to antisupernaturalist assumptions. The scholar's antisupernatural assumptions in this case have made a fair evaluation of the data impossible.