The eyes of a visiting archaeologist lit up when he was shown the 10 tiny, tarnished discs that had sat unnoticed in storage for two and a half years at a dig on a southern Japan island. He had been to archaeological sites in Italy and Egypt, and recognized the “little round things” as old coins, including a few likely dating to the Roman Empire. “I was so excited I almost forgot what I was there for, and the coins were all we talked about,” said Toshio Tsukamoto of the Gangoji Institute for Research of Cultural Property in Nara, an...