Assume the supernatural does exist, and consists of beings/forces that can interact with our natural universe in ways that are contrary to the natural laws of this universe (at least as we know them).
Take any generic or historical example of the supernatural, such as miracles, spiritual/supernatural revelations, sixth senses (in some contexts), angels/demons, various explanations of God/gods, vampires/werewolves, etc. Whichever you like or is your favorite. In general, you just need a being which exists in another dimension/plane of existance, and can at least one-way interact with ours in a way that "breaks" the laws of nature.
What evidence can exist or could be captured for these beings/forces/events truly being supernatural? Is it possible that they could be scientifically tested or proven? To what level or extent?
Any supernatural event which is observable (a faith healing, for example) could have witnesses, which provides some amount of legal/historical evidence, but is there any way to extend this into a more rigorous scientific test? For example, if we were able to know that a supernatural event was going to occur at a given time, and capture whatever data we desire, can this ever rise to a higher level of proof than the courtroom style proof?
Note: This probably applies to many other similar questions, such as proof for one of the many multi-verse hypotheses, proof for free will/dualism, etc. I think it may also work for proof of alien encounters...