An increasing number of power electronic applications require high power density. Therefore, the switching frequency and switching speed have to be raised considerably. However, the very fast switching transients induce a strong voltage and current ringing. In this work, a novel damping concept is introduced where the parasitic wiring inductances are advantageously magnetically coupled with a damping layer for attenuating these unwanted oscillations. The proposed damping layer can be implemented using standard materials and printed circuit board manufacturing processes. The system behavior is analyzed in detail and design guidelines for a damping layer with optimized RC termination network are given. The effectiveness of the introduced layer is determined by layout parasitics which are calculated by application of the Partial Element Equivalent Circuit (PEEC) simulation method. Finally, simulations and measurements on a laboratory prototype demonstrate the good performance of the proposed damping approach.