Silent Skies Act of 2013 - Directs the Administrator of the Federal Aviation Administration (FAA) to enter into a competitive cooperative agreement with an institution, entity, or consortium to carry out a program for the development of aircraft technology that will assist in-service and in-production civil turbojets not meeting stage 4 noise standards to comply with them or with more stringent noise standards.

Directs the Secretary of Transportation (DOT) to issue regulations to establish minimum standards to ensure that graduated percentages of civil turbojets weighing over 75,000 pounds comply with the stage 4 noise levels by specified dates.

Requires the Secretary to request the International Civil Aviation Organization to add to its Work Programme the consideration of international standards for the phase-out of aircraft not complying with stage 4 noise levels.

Declares that the requirements of this Act shall not apply to civil turbojet aircraft that operate outside of the 48 contiguous states.