Safe and Reliable Air Travel Act of 2013 - Amends the Balanced Budget and Emergency Deficit Control Act of 1985 (Gramm-Rudman-Hollings Act) to exempt from reduction, under any sequestration ordered by the President, funds made available for the operation of: (1) air traffic control towers by the Federal Aviation Administration (FAA), including compensation paid to FAA air traffic control personnel; and (2) contract air traffic control towers.