Support Our Armed Forces Act - Expresses the sense of Congress that: (1) all Department of Defense (DOD) and Coast Guard civilian employees, including military technicians (dual status), and all defense contractor employees provide vital support to the Armed Forces; and (2) all members of the reserve components of the Armed Forces who perform inactive-duty training or annual training during a government shutdown should be paid for performing such duty, just as other members of the Armed Forces who perform active service will be paid.

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 members of the Armed Forces, including reserve components, who perform inactive-duty training or annual training (under such Act only members performing active service) during such period;
• pay and allowances to all civilian personnel of DOD (and the Department of Homeland Security [DHS] in the case of the Coast Guard), including military technicians (dual status), non-dual status technicians, and federally-reimbursed state civilian employees supporting the National Guard (under such Act only personnel whom the Secretary concerned determines are providing support to members of the Armed Forces performing active service); and
• compensation to all employees of DOD and DHS contractors who are performing activities under a contract with DOD, or DHS in the case of the Coast Guard (under such Act only contractors whom the Secretary concerned determines are providing support to members of the Armed Forces performing active service).