Miracle claims are on shaky epistemic grounds. How do you confirm it was a miracle and not someone being mistaken about some phenomenon? Or more likely, that they don't have enough knowledge of the physical or cognitive sciences to know whether some phenomenon is possible or miraculous?

The proper use of humility is to take into account that we are human beings and we make mistakes and we have insufficient information, so we should try to anticipate our mistakes or lack of info and correct for them in advance. Meaning that one should have the prior for "I'm a flawed human being" higher than the prior that something was a miracle. Indeed, one should always take into account alternative explanations.