The development of quantum technologies is one of the big challenges in modern research. A crucial component for many applications is an efficient, coherent spin–photon interface, and coupling single-color centers in thin diamond membranes to a microcavity is a promising approach. To structure such micrometer thin single-crystal diamond (SCD) membranes with a good quality, it is important to minimize defects originating from polishing or etching procedures. Here, we report on the fabrication of SCD membranes, with various diameters, exhibiting a low surface roughness down to 0.4 nm on a small area scale, by etching through a diamond bulk mask with angled holes. A significant reduction in pits induced by micromasking and polishing damages was accomplished by the application of alternating Ar/Cl2 + O2 dry etching steps. By a variation of etching parameters regarding the Ar/Cl2 step, an enhanced planarization of the surface was obtained, in particular, for surfaces with a higher initial surface roughness of several nanometers. Furthermore, we present the successful bonding of an SCD membrane via van der Waals forces on a cavity mirror and perform finesse measurements which yielded values between 500 and 5000, depending on the position and hence on the membrane thickness. Our results are promising for, e.g., an efficient spin–photon interface.