Pay our Guardsmen and Civilian Defense Personnel Act - Amends the Pay Our Military Act (P.L. 113-39) to make FY2014 continuing appropriations for any period during which interim or full-year appropriations for FY2014 are not in effect to provide for pay and allowances to: (1) members of the Armed Forces, including reserve components, who perform inactive-duty training (under such Act only members performing active service) during such period; and (2) all civilian personnel of DOD (and the Department of Homeland Security [DHS] in the case of the Coast Guard), including all military technicians (dual status).