We report experimental, theoretical and molecular simulation results for the effects of confinement in a well-characterized pore on liquid-liquid separation in mixtures. The experimental measurements are for nitrobenzene/n-hexane mixtures in controlled pore glasses having diameters of 100 and 150 nm. The coexistence curves are determined by light transmission measurements, and by measurements of the nonlinear dielectric effect (NDE). Confinement is found to depress the critical mixing temperature, and the critical mixing composition is shifted towards the hexane-rich side, the effect being larger for the smaller pore. NDE measurements along the (pore) critical composition line show finite size effects due to the limitation placed on the growth of the correlation length, The theoretical and simulation results confirm these qualitative trends, Density functional theory results are presented for both symmetrical and unsymmetrical Lennard-Jones (LJ) mixtures which exhibit liquid-liquid separation in slit carbon pens. The simulation results, which are obtained using a histogram-weighting method in the Semi-Grand Ensemble, provide results for symmetrical LJ mixtures in cylindrical pores.