There are very few proven Roman mining sites, but pretty good evidence that there was a lot of Roman mineral extraction going on. Mendip lead is a good example - all the infrastructure of roads, settlements, etc, but where was the lead actually being dug? In many cases the evidence will have been destroyed by later more intensive workings.
It is unlikely miners of the time would have been leaving dateable items like bits of Samian ware or coins lying around in their workings. Radiocarbon dating is probably the best chance of getting a date, and the best source of that could be fire-setting (assuming Romans did this).
Staffordshire china is correct in saying that "ancient" workings have frequently been attributed to Romans, out of pure supposition.
A Surrey stone quarry was once believed to be Roman simply because a stone built vault in an entrance tunnel had what looked like roman numerals scratched into it, so we laughed at the idea. Then a proven Roman tile kiln turned up, the structure of which contained four very substantial blocks of the same local stone in it. We have no idea where the blocks might have been quarried, but no longer can we laugh at the idea that Romans were quarrying the local stone. Supposition is a dangerous game, and it can work both ways.