Highly conductive porous media have recently been considered for enhanced cooling applications due to their large internal contact surface area, which promotes convection at the pore level. In this paper, graphite foams that possess high thermal conductivity but low permeability are investigated for convection heat transfer enhancement using air as coolant. Two novel heat sink structures are designed to reduce the fluid pressure drop. Both experimental and numerical approaches are adopted in the study. The experimental data show that the designed structures significantly reduce flow resistance in graphite foams while maintaining relatively good heat removal performance. The numerical results obtained based on the local thermal nonequilibrium model are validated by experimental data and show that the inlet air flow partially penetrates the structured foam walls, while the remaining air flows tortuously through slots in the structure. Flow mixing, which is absent in the block graphite foam, is observed in the freestream area inside the designed structure. It can be concluded that graphite foams with appropriately designed structures can be applied as air-cooled heat sinks in thermal management applications.