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The temperature rise in AlGaN/GaN high-electron-mobility transistors depends strongly on the GaN-substrate thermal interface resistance (TIR). We apply picosecond time-domain thermoreflectance measurements to GaN-SiC composite substrates with varying GaN thickness to extract both the TIR and the intrinsic GaN thermal conductivity at room temperature. Two complementary data extraction methodologies yield 4-5 for the GaN-SiC TIR and 157-182 for the GaN conductivity. The GaN-SiC interface resistance values reported here, as well as the TIR experimental uncertainties documented in this letter, are substantially lower than those reported previously for this material combination.