Eddy current brakes are nowadays only used in special applications, although they have enormous advantages over conventional brakes: low wear, no generation of fine dust and excellent control possibilities. The basic principle of the eddy current brake is comparatively simple, but the details and mutual influences of the physical effects are more complex. Depending on the rotation speed and magnetic excitation, there are locally very different magnetizations, eddy currents and losses. The electromagnetic and thermal effects can therefore by no means be quantified analytically, so that numerical simulation using the finite element method (FEM) is resorted to for the calculation. In addition to the field simulation, the entire behavior can also be considered in a system simulation. The electromagnetic model is transformed into a nonlinear, static Reduced Order Model (ROM) and the thermal model into a linear, transient ROM. The two ROMs exchange loss and temperature coefficients and can calculate an entire driving cycle in seconds. This system model thus allows to be used as a digital twin to directly obtain system responses (braking torque, temperature, etc.) using virtual sensors and to be integrated into a control process. The presentation illustrates the possibilities of a FEM field simulation for the design of a wear- as well as dust-free eddy current brake, procedures for the reduction of the field models and the use of a system simulation as a digital twin.