Heat transfer experiments were performed in a vacuum environment (0.045 torr) to find out solid spot contact conductance for nominally flat surfaces of copper, brass, and stainless steel with different surface roughnesses (1-5 m) for each specimen under several load conditions (0.6-15MPa). A precise estimation of thermal contact conductance for the interface of sets of similar materials has been carried out employing a steady-state approach. Results have been compared with the theoretical models based on plastic and elastic deformation based theories for nominally flat metallic contacts. It has been demonstrated that a dire need exists to develop an experimentally based generalized correlation of thermal contact conductance for nominally flat metallic contacts that can be used by design engineers as well as for research purposes in different fields. Along with the generalized correlation, a specific correlation for thermal contact conductance has been proposed for three sets of materials. The thermal contact conductance of each set of materials presented in the form of specific correlations for different roughness parameters is one of the most important outcomes of the present research.