Nonlaminated magnetic actuators are highly influenced by eddy currents and minor perturbations like e. g. hysteresis. Known analytical models lead to trans-cendental system descriptions with fractional-order characteristics, not suited for the actuator control. Although analytical approximations resolve the issue, the inclusion of minor perturbations leads to impractical model orders, which require simplifications and compromise the model accuracy. This article studies numerical methods to directly approximate the transcendental systems or measurement data, allowing for a high accuracy with sufficiently low orders. We improve existing approaches like Levy’s method and vector fitting and apply them to a fractional-order system. Using measurement data, a comparison shows that the numerical approaches match or excel our previously studied analytical approximations.