We have studied the evolution, with hydrostatic pressure, of the recently discovered superconductivity in the graphite intercalation compounds C\(_6\)Yb and C\(_6\)Ca. We present pressure-temperature phase diagrams, for both superconductors, established by electrical transport and magnetization measurements. In the range 0-1.2 GPa the superconducting transition temperature increases linearly with pressure in both materials with \(dT_c/dP = +0.39 K/GPa\) and \(dT_c/dP = +0.50 K/GPa\) for C\(_6\)Yb and C\(_6\)Ca respectively. The transition temperature in C\(_6\)Yb, which has beenmeasured up to 2.3 GPa, reaches a peak at around 1.8 GPa and then starts to drop. We also discuss how this pressure dependence may be explained within a plasmon pairing mechanism.