An integrated experimental and numerical investigation of the thermal contact resistance across two nominally flat, coated metallic engineering surfaces in contact is presented. The model consists of a surface deformation computation, which determines the actual contact area and number of contacting asperities at a joint, and a constriction resistance analysis, which determines the constriction resistance through each individual contacting asperity. Predictions from the model are validated against experiments conducted for the purpose. The experiments are performed according to a "design of experiments" approach and evaluated using statistical regression. Three substrates (copper, brass, and aluminum) and three coatings (silver, nickel, and tin) are considered with a variety of coating thicknesses and substrate roughnesses. The contact load is also varied. The experimental measurements show that the best choice of a coating for contact resistance mitigation depends on the substrate material and roughness, and it cannot be prescribed in general. A regression equation developed for the experimental results offers a useful tool for the design of coated contacts. The measured results agree well with predicted values from the numerical model, especially in cases of a rough substrate or hard coating.