A robust supervisory control problem first addressed by \textit{J. E. R. Cury} and \textit{B. H. Krogh} [IEEE Trans. Autom. Control 44, 376--379 (1999; Zbl 1056.93563)] is considered. The problem is to synthesize a supervisor for the nominal plant model which maximizes robustness. In the article the partial observation case is considered, and the specification is described by prefix-closed languages. First, a supervisor that maximizes robustness is synthesized. This result shows that robustness can be optimized under partial observation. Next, in a special case, where all the controllable events are observable, a problem of permissiveness is solved as well. In this case the maximally permissive supervisor for the nominal plant model which maximizes not only the robustness but also permissiveness for the maximal set of admissible plant variations is synthesized.