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This manuscript describes a systematic and rational design of an experimental apparatus based on ASTM D-5470 standard for thermal interface resistance measurement of high performance thermal interface materials (TIM). The apparatus is intended to provide measurement of TIM thermal resistance as low as 0.065 K-cm2/W within 10% experimental uncertainty. The key points addressed are: 1) Apparatus design to obtain accurate measurement of TIM surface temperatures and heat flux, 2) Effects of surface flatness and roughness, and 3) Importance of and methods for surface cleaning. Design criteria are presented for choosing temperature sensors, their installation method, meter-bar material and thickness. The temperature sensors in the meter-bars should be located a sufficient distance from the heaters to ensure uniform heat flux in the thermal sensor region. Cooling plate design specifications, and a method for applying interface pressure are described. Experimental data are presented on a new TIM having 0.058 K-cm2/W interface resistance with 138 kPa contact pressure, which is lower than commercially available thermal grease and phase change materials.