Thermal contact resistances between a silver metallized SiC chip and a Molybdenum substrate and between the Molybdenum substrate and bulk Copper were measured in a heat transfer experiment. An experimental method to separate thermal contact resistances in a multilayer heat transfer path was used to extract the layer-specific contact resistances. The experimental results were compared with theory based calculations and also with 3-D computational fluid dynamics (CFD) simulation results. The results show significant pressure dependence of the thermal contact resistance and the results show higher thermal contact resistance per unit area between the bulk SiC chip and Molybdenum than between Molybdenum and bulk Copper.