The state courts, under the saving to suitors clause, can entertain suits in both equity and at law.   The right of a common law remedy includes all means except admiralty proceedings that may be employed to enforce the right or redress the injury involved.  It also includes judicial remedies conferred by statute, as well as those existing at common law, remedies in equity, as well as those enforceable in a court of law.[i]  Since admiralty courts do not have jurisdiction of primarily equitable claims, jurisdiction of state courts over an equitable claim arising from a maritime matter exists independently of the saving to suitor clause.

[i] Lewis v. Lewis & Clark Marine, Inc., 531 U.S. 438 (U.S. 2001)