Radio surveys of supernova remnants (SNRs) in the Galaxy have uncovered 19 SNRs accompanied by OH maser emission at 1720 MHz. This unusual class of maser sources is suggested to be produced behind a shock front from the expansion of a supernova remnant running into a molecular cloud. An important ingredient of this model is that X-ray emission from the remnant enhances the production of OH molecules. The role of X-ray emission from maser-emitting (ME) SNRs is investigated by comparing the X-ray-induced ionization rate with the theory. One aspect of this model is verified: there is a strong association between ME and mixed-morphology or thermal composite SNRs - center-filled thermal X-ray emission surrounded by shell-like radio morphology. We also present ROSAT and ASCA observations of two ME SNRs: G21.8-0.6 (Kes 69) and G357.7-0.1 (Tornado).