This paper presents a system-level model of a microsystem architecture deploying cooperating microactuators. An assembly of a piezoelectric kick-actuator and an electromagnetic catch-actuator manipulates a structurally unconnected, magnetized micromirror. The absence of mechanical connections allows for large deflections and multistability. Closed-loop feedback control allows this setup to achieve high accuracy, but requires fast and precise system-level models of each component. Such models can be generated directly from large-scale finite element (FE) models via mathematical methods of model order reduction (MOR). A special challenge lies in reducing a nonlinear multiphysical FE model of a piezoelectric kick-actuator and its mechanical contact to a micromirror, which is modeled as a rigid body. We propose to separate the actuator–micromirror system into two single-body systems. This step allows us to apply the contact-induced forces as inputs to each sub-system and, thus, avoid the nonlinear FE model. Rather, we have the linear model with nonlinear input, to which established linear MOR methods can be applied. Comparisons between the reference FE model and the reduced order model demonstrate the feasibility of the proposed methodology. Finally, a system-level simulation of the whole assembly, including two actuators, a micromirror and a simple control circuitry, is presented.