Marine and Hydrokinetic Renewable Energy Promotion Act of 2014 - Amends the Energy Independence and Security Act of 2007 to require the program of marine and hydrokinetic renewable energy technology research, development, demonstration, and commercial application to: (1) apply advanced systems engineering and system integration methods to identify critical interfaces and develop open standards for such renewable energy; (2) transfer the resulting environmental data to industry stakeholders as public information through published interface definitions, standards, and demonstration projects; and (3) develop incentives for industry to comply with the standards.

Requires the Department of Energy (DOE) to award grants to support modifying or constructing four or more geographically dispersed marine and hydrokinetic renewable energy technology research, development, and demonstration test facilities for the demonstration of multiple technologies in actual operating environments. Requires DOE to give preference to existing facilities and National Marine Renewable Energy Research, Development, and Demonstration Centers.

Renames the Centers as the "National Marine and Hydrokinetic Renewable Energy Research, Development, and Demonstration Centers" and expands their research and clearinghouse duties to include hydrokinetic energy. Authorizes the Centers to serve as technology test facilities.

Requires DOE to establish a marine-based energy device verification program to provide a bridge from marine and hydrokinetic renewable energy capture device design and development efforts to commercial deployment.

Requires DOE to establish a grant program to advance the development of marine and hydrokinetic renewable energy and associated devises and technologies.

Authorizes appropriations for the marine and hydrokinetic renewable energy technologies program through FY2016.