The coronagraphic instrument (CGI) currently proposed for the Wide-Field Infrared Survey Telescope–Astrophysics Focused Telescope Assets (WFIRST-AFTA) mission will be the first example of a space-based coronagraph optimized for extremely high contrasts that are required for the direct imaging of exoplanets reflecting the light of their host star. While the design of this instrument is still in progress, this early stage of development is a particularly beneficial time to consider the operation of such an instrument. We review current or planned operations on the Hubble Space Telescope and the James Webb Space Telescope with a focus on which operational aspects will have relevance to the planned WFIRST-AFTA CGI. We identify five key aspects of operations that will require attention: (1) detector health and evolution, (2) wavefront control, (3) observing strategies/postprocessing, (4) astrometric precision/target acquisition, and (5) polarimetry. We make suggestions on a path forward for each of these items.