The polarizable embedding (PE) approach, which combines quantum mechanics (QM) and molecular mechanics (MM), is applied to predict solvatochromic effects on excitation energies of several representative molecules in aqueous, methanol, acetonitrile, and carbon tetrachloride solutions. Good agreement with experimental results for excitation energies and for solvatochromic shifts is demonstrated on the basis of either density functional theory or coupled cluster methods. Solvent-dependent trends are fully reproduced in this diverse set of solvents. Furthermore, it is shown that the inclusion of higher order multipole moments and anisotropic polarizabilities in the electrostatic embedding potentials leads to a faster convergence with respect to a full QM treatment (within about 0.1 eV of estimated full QM treatments). It is thereby illustrated that the use of advanced solvent potentials can provide higher accuracy compared to various simpler approaches for the prediction of solvent shifts and do so in a computationally competitive manner.