The "largest naval battle in history" is a disputed title between adherents of varying criteria which include the numbers of personnel and/or vessels involved in the naval battle, the total displacement of the vessels involved and sometimes the significance and/or implications of the battle. While battles fought in modern times are comparatively well-documented, the figures from those in pre-Renaissance era are generally believed by contemporary chroniclers to be exaggerated.
A romantic style painting of the Battle of Salamis by Wilhelm von Kaulbach
The Battle of Cape Ecnomus or Eknomos was a naval battle, fought off southern Sicily, in 256 BC, between the fleets of Carthage and the Roman Republic, during the First Punic War. The Carthaginian fleet was commanded by Hanno and Hamilcar; the Roman fleet jointly by the consuls for the year, Marcus Atilius Regulus and Lucius Manlius Vulso Longus. It resulted in a clear victory for the Romans.
Carthaginian naval ram, c. 240 BC; note the gouges towards the bottom, probably from bow to bow contact with another vessel