Capillary forces in the pressure infiltration process can be quantified by measuring saturation curves; these are plots of the fraction pore space filled with the liquid infiltrant versus the pressure difference between the liquid and the atmosphere initially present in the porous preform to be infiltrated. We present data measured using an apparatus capable of measuring saturation curves at high temperature (≈1200°C) and high pressures (≈150 atmospheres), these being conditions suitable for the study of metal matrix composite pressure infiltration. Preforms of alumina or carbon are infiltrated with copper-based melts, varying the infiltration temperature and the alloy composition, to explore (i) the influence of the contact angle and work of immersion (reported in the literature from sessile drop experiments) on the saturation curve and consequently the ease of infiltration processing for the various systems explored and (ii) sources of irreversibility in the process that arise from geometrical and kinetic features of the infiltration process.