The subject of this paper is a non-coaxial eddy-current coupling, which can be utilized on a freight train wagon for generating auxiliary power in the range of several Watts. The coupling comprises a wheel with radially magnetized permanent magnets, which is positioned in the vicinity of the wagon's wheel, and extracts kinetic energy when the train is in motion. A computational method for solving the 3-D problem of the eddy-current coupling is presented. Maxwell's equations for calculating the excited eddy currents are solved in the Fourier domain with a semi-analytical method (SAM), resulting in computationally efficient simulations. In a case study, the SAM shows 500 times faster simulation times, compared to a 3-D transient eddy-current finite-element method simulation, carried out with a commercially available software. The SAM is verified with measurements taken on two hardware prototypes. Furthermore, in order to generalize the study, a ??-Pareto optimization of the system is conducted for relaxed design space boundaries, an output power of P = 10 W, a C45E steel wheel with v = 80 km/h surface velocity, and g = 3 mm air gap. It is shown that a power density up to 0.8 kW/dm3 (13 W/in3) and a transfer efficiency up to 60% can be achieved using the proposed system.