Surface tension plays an important role in the nucleation of H₂O gas bubbles in magmatic melts and in the time-dependent rheology of bubble-bearing magmas. Despite several experimental studies, a physics based model of the surface tension of magmatic melts in contact with H₂O is lacking. This paper employs gradient theory to develop a thermodynamical model of equilibrium surface tension of silicate melts in contact with H₂O gas at low to moderate pressures. In the last decades, this approach has been successfully applied in studies of industrial mixtures but never to magmatic systems. We calibrate and verify the model against literature experimental data, obtained by the pendant drop method, and by inverting bubble nucleation experiments using the Classical Nucleation Theory (CNT). Our model reproduces the systematic decrease in surface tension with increased H₂O pressure observed in the experiments. On the other hand, the effect of temperature is confirmed by the experiments only at high pressure. At atmospheric pressure, the model shows a decrease of surface tension with temperature. This is in contrast with a number of experimental observations and could be related to microstructural effects that cannot be reproduced by our model. Finally, our analysis indicates that the surface tension measured inverting the CNT may be lower than the value measured by the pendant drop method, most likely because of changes in surface tension controlled by the supersaturation.