A finite-difference time-domain (FDTD) method for electromagnetics, which is adapted for magnetic-field diffusion problems, has been applied for accurate calculation of the resistance and inductance of arbitrarily wound helical coils of interest in magnetic flux-compression systems. These simulations have been performed using a locally developed 3-D variable-mesh FDTD code. The resistance calculations automatically take account of skin and proximity effects and are capable of handling arbitrarily complex multimaterial systems. The simulations also yield a detailed 3-D picture of the magnetic-field diffusion through a complex multimaterial coil in the presence of arbitrary time dependent current waveforms. Hence, they can provide critical insight into coil performance in real-life systems. We report on the critical issues that must be kept in mind for such simulations and the results of test problems with simple coil geometries. To our knowledge, this is the first application of this powerful technique to the flux-compression systems.