We study electrostatic correlations in structured solvents confined to nanoscale systems. We derive variational equations of Netz-Orland type for a model liquid composed of finite size dipoles. These equations are solved for both dilute solvents and solvents at physiological concentrations in a slit nanopore geometry. Correlation effects are of major importance for the dielectric reduction and anisotropy of the solvent resulting from dipole image interactions and also lead to a reduction of van der Waals attractions between low dielectric bodies. Finally, by comparison with other recently developed self-consistent theories and experiments, we scrutinize the effect of solvent-membrane interactions on the differential capacitance of the charged liquid in contact with low dielectric substrates. The interfacial solvent depletion driven by solvent-image interactions plays the major role in the observed low values of the experimental capacitance data, while non-locality associated with the extended charge structure of solvent molecules only brings a minor contribution.