Shelter Our Servicemembers Act - Directs the Secretaries of Veterans Affairs (VA) and Housing and Urban Development (HUD) to jointly establish a two-year pilot program of grants to nonprofit organizations to provide elderly homeless veterans with non-transitional housing. Authorizes the Secretaries to award two grants of up to $25 million each under the program. Allows recipients to use such grant to: (1) purchase real property to provide up to 200 homeless veterans with non-transitional housing, and (2) refurbish or renovate such property.

Makes eligible for such housing veterans of at least 55 years of age who: (1) have been continuously homeless for a year or more or, during the last three years, had at least four separate periods of living on the streets, in an emergency shelter, or a combination thereof; and (2) have a condition that limits their ability to work or perform activities of daily living. Directs the VA Secretary to provide case management for elderly veterans receiving such assistance.