New measurements of the amount-of-substance densities rho of nine mixtures of (water + methane) are reported in the temperature range 430 K to 699 K at pressures from 7.5 MPa to 30 MPa. The results have been obtained by using a fully automated isochoric instrument. The uncertainty in the experimental results is estimated to be about +/-0.0008 .rho at the lowest water content and +/-0.0014 .rho at the highest water content. Comparisons with independent sources of experimental information through a model based on the two-fluid corresponding states principle are presented. The dew points of the mixtures studied have also been determined and compared with predicted values from the Peng-Robinson equation of state.