The melting and freezing of water in a series of mesoporous silica materials with a hexagonal arrangement of unidimensional cylindrical pores and narrow pore-size distribution (MCM-41 with pore diameters from 2.9 to 3.7 nm, and SBA-15 with pore diameters from 4.4 to 11.7 nm) was studied by differential scanning calorimetry (DSC). A lowering of the melting temperature ΔT_m = T_mb − T_m(R) up to 50 K was found for water in pores of decreasing radius R. The melting point data can be represented by a modified Gibbs–Thomson equation, ΔT_m(R) = K/(R-t), with K = 52 K nm and t = 0.4 nm, in agreement with an earlier study of water in MCM-41 materials of pore width 2 to 4 nm. The value of K agrees with an estimate of the Gibbs–Thomson constant based on thermodynamic data for the normal melting point of ice, and the parameter t can be taken as the thickness of a surface layer of non-frozen water at the pore wall. DSC scans of the freezing of H₂O and D₂O in partially filled pores of SBA-15 reveal a peak pattern depending on the degree of pore filling ϕ. The different peaks are attributed to different states of the liquid in the pore space, iz. pore water in completely filled regions, and water as an adsorbed film at the pore wall. These two states coexist in a pore filling range ϕ_min<ϕ<1, but only the film state exists at ϕ<ϕ_min. The freezing peak of pore water appears to be nucleated by external bulk ice (at ϕ>1) but exhibits substantial supercooling at ϕ<1. On the other hand, the peak attributed to the freezing of film water exhibits no significant supercooling and is found at temperatures near 237 K, almost independent of ϕ and the pore width of the SBA-15 sample. The nature of a further (small) peak near 233 K is not yet understood. Contrary to cooling scans, only one DSC peak is observed in heating scans, independent of the pore filling. This finding indicates that the adsorbed liquid film is metastable relative to the frozen pore liquid.