We report Time-Domain ThermoReflectance experiments measuring the Thermal Boundary Conductance (TBC) of interfaces between diamond and metal surfaces, based on samples consisting of [111] diamond substrates with hydrogen or with sp2 carbon surface terminations created using plasma treat- ments. In a concurrent theoretical study, we calculate the work of adhesion between Ni, Cu and diamond interfaces with [111] surface orientation, with or without hydrogen termination of the diamond surface, using first-principles electronic structure calculations based on density functional theory (DFT). We find a positive correlation between the calculated work of adhesion and the mea- sured conductance of these interfaces, suggesting that DFT could be used as a screening tool to identify metal/dielectric systems with high TBC We also explain the negative effect of hydrogen on the thermal conductance of metal/diamond interfaces.