A method for producing a surface coating (200), which reflects extreme-ultraviolet radiation, on a substrate (300). The surface coating (200) has a multilayer system (210) and the substrate (300) has a micro-electromechanical system on the face provided with the surface coating (200). The method includes: a) producing the surface coating (200) on a support (100) in the inverse order of the layers of the multilayer system (210); b) connecting the produced surface coating (200) to the substrate (300) on the face remote from the support (100); and c) releasing and removing the support (100) from the surface coating (300).