The coins shown in the jewelry pieces below are real and have been inspected and authenticated by numismatics specializing in Greek and Roman currency.
Because the Roman Empire covered such a vast geographic area for such a long time, coins such as these are not actually as hard to come by as one might think. Throughout Europe, Northern Africa and the Middle East, stashes of ancient currency like this are found every day. Buried for safe keeping by military personal in pouches or urns but never retrieved, metal detectors easily pick them up in the soil where they have sat undisturbed all this time.
Of course, there are some coins that are found which are very rare and expensive but the majority of the ones you see here are widely available on the market. For example, Alexander the Great minted some 13 million silver Tetradrachams over just an 18 year period 300 years prior to the Roman Empire. He used up to 20 talents (half a ton of silver) per day paying and rationing his army.