Current turbine airfoils must operate at extreme temperatures, which are continuously driven higher by the demand for high output engines. Internal cooling plays a key role in the longevity of gas turbine airfoils. Ribbed channels are commonly used to increase heat transfer by generating turbulence and to provide a greater convective surface area. Because of the increasing complexity in airfoil design and manufacturing, a methodology is needed to accurately measure the convection coefficient of a rib with a complex shape. Previous studies that have measured the contribution to convective heat transfer from the rib itself have used simple rib geometries. This paper presents a new methodology to measure convective heat transfer coefficients on complex ribbed surfaces. The new method was applied to a relatively simple shape so that comparisons could be made with a commonly accepted method for heat transfer measurements. A numerical analysis was performed to reduce experimental uncertainty and to verify the lumped model approximation used in the new methodology. Experimental measurements were taken in a closed-loop channel using fully rounded, discontinuous, skewed ribs oriented 45° to the flow. The channel aspect ratio was 1.7:1 and the ratio of rib height to hydraulic diameter was 0.075. Heat transfer augmentation levels relative to a smooth channel were measured to be between 4.7 and 3 for Reynolds numbers ranging from 10,000 to 100,000.