Theoretical and experimental results are presented for the effect of confinement on liquid-liquid phase equilibria for binary mixtures. Density functional theory calculations for a symmetric Lennard-Jones mixture in pores show the following qualitative features : a reduction in the critical mixing temperature, and a shift in the coexistence curve toward the component 1-rich side of the phase diagram when molecules of component 1 are more strongly attracted to the walls. These effects become more pronounced for smaller pores. Experimental results are presented for nitrobenzene/n-hexane mixtures in a controlled pore glass having pores of mean width 100 nm. Results for the liquid-liquid coexistence in the pores are obtained using nonlinear dielectric effect (NDE) and light transmission measurements. The effect of confinement is to produce a lowering of the critical mixing temperature by 0.05 +/- 0.02 K and a shift in the critical mixing composition toward the nitrobenzene-rich side of the diagram by 0.04 +/- 0.01 in mole fraction. Measurements near the pore critical point show that the NDE tends to a finite value at the critical paint, apparently due to the constraint on the growth of the correlation length due to the pore walls.