A fuel cell has a MEMS fuel-cell structure including an anode, a cathode, and an electrolyte, formed on a substrate, a portion of the substrate being removed from beneath the MEMS structure to leave the MEMS structure suspended in membrane form. An opening may extend through the substrate to leave the MEMS fuel-cell structure in a cantilevered configuration, supported by only one edge. Additional openings may be formed to relieve mechanical stress near an edge or edges supporting the MEMS fuel-cell structure, and/or to limit heat-conducting paths. Specially adapted methods are disclosed for fabricating the MEMS-based fuel cell in any of its various configurations.