Yes, there were naval battles; in fact, the first ironclad ships were invented during the Civil War.
The Union navy had naval superiority during the Civil War.
Naval battle
Naval battle
Naval Forces in support of military operations in Panama and Grenada.
Fort Sumter
The Battle of Hampton Roads.
The motto was "Don't tread on me."
Iron Bridge
The Naval blockade
The US Naval Academy is the name. It is often referred to as Annapolis, as that is where it is currently located. It was temporarily moved during the Civil War.
The naval battle during the American Civil War that involved the clash between the USS Merrimack and the USS Monitor was the Battle of Hampton Roads.