Ab initio molecular dynamics simulations predict that CaSiO3 perovskite melts at 5600 K at 136 GPa, and 6400 K at 300 GPa, significantly higher than MgSiO3 perovskite. The entropy of melting (1.8 kB per atom) is much larger than that of many silicates at ambient pressure and of simple liquids and varies little with pressure. The volume of melting decreases rapidly with increasing pressure, to 3 % at 136 GPa, producing a melting slope that diminishes rapidly with pressure. We determine the melting temperature via the ZW method, combining the Z method, for which we clarify the theoretical basis, with a waiting time analysis. The ZW method results are internally confirmed by integrating the Clausius‐Clapeyron equation, which also yields our results for the entropy and volume of melting. We find the eutectic composition on the MgSiO3‐CaSiO3 join to be xCa = 0.26 at 136 GPa and that metasilicate melt is denser than coexisting silicates.