In this paper, we present an efficient modeling and computational scheme for a repeated solution of an eddy-current system with different values of the supply frequency as well as of the permeability and conductivity of the eddy-current region. The scheme is based on a general parametric expression obtained for the finite-element (FE) solution with the supply frequency, permeability, and conductivity as parameters. The algorithm allows for numerically efficient updating of the solution for different values of the parameters through the solution of a much smaller sparse linear system, instead of a repeated solution of the entire FE model. Moreover, if required, the solution can be computed only over a small region of interest, making the scheme ideally suited to many coupled-field problems. As an application, the scheme is applied to a typical bar-plate eddy-current system, excited by nonsinusoidal currents. The time variations of the magnetic field are computed as a superposition of responses computed for a number of harmonics. An a priori estimate for the difference between responses to two harmonics has been obtained, which can be used as a frequency-sensitivity measure to avoid computation of responses to all individual harmonics. The applicability of the approach to general transient excitations and further possible developments are identified.