Phase transitions of substances confined in narrow pores are affected by finite-size effects, surface interactions and reduced dimensionality. Generally the gas/liquid transition in pores (pore condensation) is shifted to a lower pressure at constant temperature, and the liquid/solid transition (pore freezing) is shifted to a lower temperature at constant pressure (although an increase of the freezing temperature has been observed in some cases). Thermodynamics predicts that the extent of these shifts is proportional to 1/L, where L is the distance between the confining pore walls. Silica materials with ordered arrays of cylindrical mesopores of uniform size, such as MCM-41 or SBA-15, are well-suited for quantitative studies of pore condensation and pore freezing. We performed water sorption and DSC melting and freezing point measurements of normal and heavy water in a set of well-ordered MCM-41 and SBA-15 silica materials with primary pore diameters ranging from 2.5 to 10 nm, as determined by nitrogen adsorption and using the DFT kernel for the pore size determination. Narrow freezing and melting peaks are observed, which in MCM-41 samples with sufficiently narrow pores occur at temperatures well below the temperature of homogeneous nucleation of supercooled bulk water. The dependence of the melting point depression ΔT_m = T_m0–T_m(R) on the pore radius R can be represented by a modified Gibbs-Thomson equation of the form ΔT_m = K/(R – t). The resulting value of the constant K is consistent with the Gibbs-Thomson constant as derived from the thermodynamic data of water at the bulk melting temperature T_m0. For the constant t, which can be taken as the thickness of a non-freezing layer of water in contact with the pore wall, we find a value corresponding to ca. two monolayers of water. The peak area of the DSC peaks decreases strongly with decreasing pore radius, and for the sample with the smallest pore size (R = 1.3 nm) no phase transition is detected by DSC. A quantitative analysis of the DSC data indicates that the molar melting enthalpy of pore water decreases approximately as Δh ∝ R - R₀ with R₀ ≈ 1.3 nm, i.e., a stronger decrease than expected on the basis of the volume-to-surface ratio of ice in the cylindrical pores, V/A ∝ R. This observation indicates that the decrease of Δh with the pore radius is due in part to an intrinsic temperature dependence of the melting enthalpy.