Safe Exploration Coming from Underwater Reserves of Energy Act or the SECURE Act - Permits each holder of a permit to drill for oil or natural gas that was approved by the Minerals Management Service before May 3, 2010, to conduct all operations authorized under the terms of the permit: (1) without further review by the Bureau of Ocean Energy Management, Regulation and Enforcement; and (2) without further review or delay under the National Environmental Policy Act of 1969 or any other similar statutes such as the Federal Water Pollution Control Act or the Marine Mammal Protection Act of 1972.