Maritime Services Financial Responsibility Act of 1986 - Requires owners of foreign vessels engaged in foreign commerce and using U.S. ports to establish and maintain financial responsibility for claims arising from the furnishing of maritime services to those vessels. Describes the financial responsibility required and sets forth restrictions on the acceptance of bonds filed by such owners. Permits claims to be brought directly against the insurer or other person providing financial responsibility in any case where jurisdiction over such a vessel cannot be obtained under U.S. law. Sets forth fines and sanctions to which owners subject themselves for noncompliance with this Act, including port entry or clearance denial in appropriate cases.