Inelastic neutron scattering has been employed to probe the vibrational density of states of water confined by an oxide surface, namely, nanoparticles of the anatase polymorph of TiO2. The heat capacity of confined water has been measured by adiabatic calorimetry and compared with values derived from the vibrational density of states. Both inelastic neutron scattering and calorimetry demonstrate restricted mobility and lower heat capacity and entropy of confined water as compared to the bulk.