We have an understanding of how we expect the world to work. This gives us a base level on interpreting anomalous events. The label miracle can be used for so much, but in general it's shorthand for what we consider a violation of how the world works. So if we have a conception of how the world works, and there's a violation of that conception, that proves a miracle, right?
Well, no. Massimo Pigliucci in his book Nonsense On Stilts gives an account of why this isn't so. While I recommend the book, I'll try to illustrate here his argument.
Imagine a violation of nature took place, a glass of water before the eyes of many turned into wine. Magicians were on hand to witness there was no foul play - they could not detect any. Many scientists did chemical analyses of the contents of the glass, showing that there was pure water before the transformation, and wine after the transformation. In other words, there was no possible explanation anyone could come up with to explain what had transpired.
In this case it seems pretty clear that a miracle happened. It's not even that it's not yet explained, but that it was in violation of what was known about nature. There lingered the possibility of foul play, but none could be detected and the exercise was conducted in such a way that it could not be regarded as having happened - the best one could have is the suspicion of foul play. So does this prove it was a miracle?
Again, no. Miracle in this sense is not an explanation, but merely a label of ignorance. Since we don't know what happened, how can we say it's caused by supernatural intervention? We can say that what happened is in violation of what is known about the natural, but that just means that perhaps our conception of the natural is lacking. To get to the supernatural from the natural would mean having to discount all possible natural explanations, a task which is impossible for the simple fact that we don't know everything about everything.
If we're going to call the miraculous as violations of nature, then we're left with the impossible task of proving that such events took place. Because violates what is known about nature doesn't mean that it's not natural, but this is what happens when one deals in negative definitions. You just can't use science to prove the miraculous, for all you've done is say that science says we don't know.