We introduce an enhanced parametric model for a copper-layered eddy current electric machine (retarder) for automotive braking applications. The modeled torque characteristics of the copper-layered electromagnetic retarders are based on the results from a detailed electromagnetic finite element analysis (FEA) of these eddy current machines. The model uses a parameterized double-exponential function to model the steady state speed-torque characteristics of the retarder. The parameters are adjusted for optimal braking performance in conjunction with predicted speed-torque characteristics of a copper-layered retarder. A full vehicle model, along with the proposed retarder speed-torque model has been used to simulate a series braking events. The simulation results show that the peaks of the retarder speed-torque curves must be designed to occur within a specific range of speeds for optimal braking performance