Ships with wind-assisted propulsion systems (WAPS) are often equipped with large rudders to compensate for WAPS-induced drifting forces. The WAPS also significantly affects the effectiveness of mathematical models used to describe the ship's maneuvering characteristics. In this study, a modular maneuvering model is proposed to enhance the original MMG model, with the aim of producing accurate maneuvering simulations for ships with WAPS. Methods of virtual captive tests (VCT) are proposed to recreate the forces acting on WAPS ships during free-running model tests (FRMT) in motor mode, identifying all the parameters in the modular model. The hydrodynamic damping coefficients within the model are determined through linear regression of the VCT data. The added masses are then determined from pure yaw and pure sway simulations using a fully nonlinear potential flow (FNPF) panel method. Two ships designed for WAPS, wPCC and Optiwise, are used to validate the proposed method based on the inverse dynamics of their experimental model tests. The wPCC is equipped with a semi-empirical rudder that has previously shown to work well for this twin-rudder ship. The Optiwise single rudder is modeled with a new quadratic version of the MMG rudder model, proposed in this paper. Inverse dynamics analysis, together with state VCTs, is concluded to be an efficient way to analyze the models, and the maneuvering model can be efficiently identified when the correct VCTs are used in the proposed method. However, the inverse dynamics analysis also revealed potential errors in the wPCC VCT data due to false assumptions about wave generation and roll motion. The Optiwise test case, where these assumptions should be more valid, showed much better agreement with the FRMT inverse dynamics.