National Silver Alert Act of 2013 - Directs the Attorney General to: (1) establish a national Silver Alert communications network within the Department of Justice (DOJ) to assist regional and local search efforts for missing seniors; (2) ensure that, when feasible, the network is able to operate in coordination with the AMBER Alert communications network; and (3) designate an individual of DOJ to serve as the Silver Alert Coordinator to coordinate the network with states. Defines "missing senior" as any individual who is reported as missing to or by a law enforcement agency and who meets state requirements for designation as a missing senior.

Directs the Coordinator to: (1) establish minimum standards for the issuance and dissemination of alerts issued through the network; and (2) make available to states, local governments, law enforcement agencies, and other concerned entities network training and information.