Differential phase-contrast imaging with hard x rays can have important applications in medicine, material sciences, and energy research. Phase-contrast methods based on microperiodic optics, such as shearing interferometry, are particularly attractive because they allow the use of conventional x-ray tubes. To enable shearing interferometry with x rays up to $100\mathrm{keV}$ , we propose using grazing- incidence microperiodic mirrors. In addition, a simple lithographic method is proposed for the production of the microperiodic x-ray mirrors, based on the difference in grazing-incidence reflectivity between a low-Z substrate and a high-Z film. Using this method, we produced prototype mirrors with $5–100\mathrm{\mu m}$ periods and $90\mathrm{mm}$ active length. Experimental tests with x rays up to $60\mathrm{keV}$ indicate good microperiodic mirror reflectivity and high-contrast fringe patterns, encouraging further development of the proposed imaging concept.