Ensuring Safe Shelter for Homeless Veterans Act of 2013 - Prohibits a per diem payment from being made to providers of services for homeless veterans unless the Secretary of Veterans Affairs (VA) certifies that: (1) the building where the entity provides housing or services is in compliance with codes relevant to the operations and level of care provided; and (2) such building and the housing or services provided are in compliance with licensing, fire and safety, and other requirements of the relevant jurisdiction regarding the condition of the building and the provision of such housing or services.

Authorizes the Secretary to revoke any certification upon determining that it is no longer accurate. Requires the Secretary to: (1) inspect such facilities at least annually, and (2) notify Congress of any such revocation and termination of per diem payments.

Requires the Secretary's annual report on assistance to homeless veterans to include an evaluation of the safety and accessibility of such providers' facilities.

Directs the Secretary to assess the compliance of the building and housing and services provided by current per diem payment recipients. Prohibits additional payments to a recipient that is not, within two years after enactment of this Act, certified to be in compliance until the Secretary certifies that the building and housing and services provided are in compliance.