Based on information provided by others, miracles fall into one of two large categories. Those that defy the laws of nature and those that defy probability.
Since people declare things are miracles, I am assuming some of them know the difference between ordinary events and events that are miracles. What I am hoping to see are the details that they use to make that determination. What I am finding is that I am not alone in my ignorance of those details and characteristics. It seems that in most of those instances, the details are unknown and belief that of the event as a miracles is the defining character. I am also not sure that it matters, just so long as you don't start making claims that cannot be backed up. This, in my mind, takes it to some level of false witness that I am enjoined (as presumably they are too) from engaging in.
I am an Atheist so if I was presented with what appeared to be a genuine miracle, as I believe that they are essentially impossible because I assume natural laws are universal, it would cause a major rupture in my own worldview and would cause a great deal of confusion and soul-searching.
If I were to approach the issue as if I were a Christian, my suggestion is that faith is based on recognising the limits of our knowledge and the scope of our ignorance. We're only human and we can only work with the limited knowledge and tools to understand the world around us. Our knowledge is not absolute and sometimes we have to work with the imperfect answers we have rather than the perfect answers we would wish to have.
I'm definitely not a fan of those who argue that somethings are inherently beyond our understanding, but sometimes we don't know and that isn't a personal failure on our part. Even if everything can be seen, observed and understood, the world is too big for us to understand it all. We might dedicate our entire lives to the pursuit of knowledge but we would will still die with the work of discovery left unfinished. We are allowed to be imperfect and to get things wrong. We have the right to forgive ourselves for not always understanding clearly. For the most part, we just have to do our best to get the little part we play right for however long we are here.