Uncharted Waters: New Horizons

From the SNES box:

Imagine a time when mighty navies controlled the seven seas, ruthless pirates searched for hidden treasures and scholars argued that the Earth was round. Now Picture yourself as a young explorer on a mission that will carry you to the four corners of the globe.

Play the son of a Portuguese Duke out to discover the legendary land of Atlantis, a Spanish female navy lieutenant turned pirate, a British privateer comissioned by Henry VIII to destroy the Spanish fleet, an Italian adventurer in debt from his father or a Turkish orphan starting his own trading business.

Your adventure will take you to over 130 exotic destinations. Along the way, you will discover exotic monuments, long sought treasures and valuable merchandise to trade. As Captain of your fleet, keep a careful eye on the horizon for pirates eager to steal your valued cargo or an enemy navy at war with the flag of your ship flies. Once in port, remember to recruit mates, purchase new ships and gunnery, gather useful information and settle disputes with your enemies by challenging them to a duel.

Get ready for the adventure of a lifetime!

From Wikipedia

Known as Daikoukai Jidai II in Japan, this game is perhaps the most famous of the series. Even though an English version exists, it still has not managed to achieve the mainstream popularity Pirates! had. There is only a relatively small following outside of East Asia.