This paper discusses the co-design of an electric aircraft propulsion system for minimum weight and maximum power-to-thrust efficiency. The system under consideration for preliminary exploration of the methodology consists of a fully superconducting synchronous motor and a ducted, fixed-pitch propeller. In order to ensure a viable propulsor, a minimum required thrust bound is imposed on the system design. Both analytical methods and finite-element analysis (FEA) are used to size the motor, and a blade-element momentum (BEM) model is implemented for predicting performance of the ducted propeller. A genetic algorithm optimization scheme is applied on a hydrogen-powered electric aircraft propulsion system proposed for the Center for High-Efficiency Electrical Technologies for Aircraft (CHEETA) project. Sensitivity of the combined system efficiency to motor weight is evaluated.