An optimal design problem of an electromagnetic actuator is formulated by defining the set of design variables, the constraints, and the optimality criterion. Solving such a problem is a difficult and time-expensive task when many variables, constraints, and conflicting objectives are involved, and when high accuracy is required. In order to determine the solution in an efficient manner, the space mapping technique is investigated. A cylindrical voice coil actuator is chosen as a proof-of-concept example. The numerical results show that the approach is viable, and an obtained design is verified by measurements.