FAMS Augmentation Act of 2013 - Directs the Assistant Secretary of Homeland Security (DHS) for the Transportation Security Administration (TSA) to increase the number of federal air marshals by at least an additional 1,750 above the number of such marshals as of January 31, 2011, to ensure increased transportation security for inbound international flights.

Declares the goal of this Act is to increase the number of inbound flights with federal marshals onboard while maintaining federal marshal presence on domestic point-to-point flights at or above December 25, 2009, levels.

Directs the Federal Air Marshal Service (FAMS) to establish a policy requiring newly hired federal air marshals to complete as part of their basic training the criminal investigative training program at the Federal Law Enforcement Training Center. Requires federal air marshals hired before enactment of this Act who have not completed such program to attend an alternative training program.

Directs the Assistant Secretary to establish in FAMS an Office of the Ombudsman.