This paper presents the modeling and design of an actuator consisting of an electrical motor and a magnetic gear. To minimize the overall actuator dimensions, both of the electromagnetic devices need to be optimally designed and matched. An issue in performing a simultaneous design as such arises from a high number of design variables that significantly increases the complexity of the optimization problem. A method to reduce the design variables is discussed in this paper, which is the application of response surface methodology (RSM) to represent the optimized torques of the electrical motor and magnetic gear as polynomial functions of their respective dimensions. Prior to the application of RSM, optimization problem statements are defined for the electrical motor and magnetic gear, for which the optimization objective and constraint functions are derived from analytical electromagnetic models of the considered electromagnetic devices.