Isochoric heat capacities of H2O+NaCl solutions (0.0031 and 0.0063 mole fraction of NaCl) were measured with a high temperature and high pressure adiabatic calorimeter near the sub-critical and near the supercritical point of pure water. Temperatures ranged from 361 to 677 K. Measurements were made at six densities, namely: 367.07 and 485.59 kg.m(-3) for x = 0.0031 mol fraction of NaCl and 388.65, 560.03, 607.05, and 973.70 kg.m(-3) for x = 0.0063 mol fraction of NaCl. Measurements were conducted in the two- and one-phase regions including near phase transition temperatures T-S(rho). The phase transition temperatures T-S(rho) and saturated isochoric heat capacity values C-VX have been determined for each isochore. The uncertainty in heat capacity measurements is estimated to be 3.5% to 4.5% near the phase transition and critical points. Present and previous results of heat capacity measurements were compared with predictions from the crossover (CREOS) and Pitzer-Tanger-Hovey equations of state (PTH EOS). Our previous heat capacity measurements were found to deviate systematically from crossover-model predictions. The present results show good agreement with the crossover model for the composition x = 0.0031 mol fraction.