In a study designed to investigate the melting behaviour of natural gas hydrates which are usually formed in porous mineral sediments rather than in bulk, hydrate phase equilibria for binary methane and water mixtures were studied using high-pressure differential scanning calorimetry in mesoporous and macroporous silica particles having controlled pore sizes ranging from 8.5 nm to 195.7 nm. A dynamic oscillating temperature method was used to form methane hydrates reproducibly and then determine their decomposition behaviour—melting points and enthalpies of melting. Significant decreases in dissociation temperature were observed as the pore size decreased (over 6 K for 8.5 nm pores). This behaviour is consistent with the Gibbs–Thomson equation, which was used to determine hydrate–water interfacial energies. The melting data up to 50 MPa indicated a strong, essentially logarithmic, dependence on pressure, which here has been ascribed to the pressure dependence of the interfacial energy in the confined media. An empirical modification of the Gibbs–Thomson equation is proposed to include this effect.