We have investigated and modeled the magnetization process in thin amorphous and nanocrystalline ribbons from DC to 1 GHz. These transverse anisotropy laminations, their thickness ranging between 6 and 20 μm, display excellent broadband magnetic behavior, ensuing from the dominant role of magnetization rotations. Combination of fluxmetric, aftereffect, and high-speed magneto-optical experiments put in evidence that the domain wall processes, the obvious source of losses at low and medium frequencies in spite of negligible contribution to the magnetization reversal, fully damp on attaining the MHz range. Here the energy dissipation chiefly descends from the rotations and conforms to the so-called classical regime. To describe the high-frequency spin dynamics, the coupled Maxwell and Landau-Lifshitz-Gilbert equations are therefore considered. We have worked out a numerical solution of such equations by a finite element approach, based on a very fine time discretization and a computing scheme preserving the magnetization modulus. From the calculation of hysteresis loop and eddy current density at each mesh point, the separate contributions to the rotational losses by the eddy currents and the spin damping mechanism are obtained. The overall energy loss behavior versus frequency is thus eventually predicted in terms of separate contributions by the domain wall processes and the rotations.