Both of these were bought at auctions or from coin dealers specializing in ancient coins :) The large one was bough on vcoins where you can generally trust the coins to be authentic.

The boring and somewhat useless answer to how I know they are authentic is experience - I’ve spent the better part of a decade collecting ancient coins, reading about ancient coins, and trading ancient coins…

Back when I started this community I copied a nice post from reddit on how to spot fakes.