We present a detailed analysis of our recently proposed wavefunction in density functional theory method to include differential polarization effects through state-specific embedding potentials. We study methylenecyclopropene and acrolein in water by using several wavefunction approaches to validate the supermolecular reference and to assess their response to embedding. We find that quantum Monte Carlo, complete-active space second-order perturbation theory, and coupled cluster methods give very consistent solvatochromic shifts and a similar response to embedding. Our scheme corrects the excitation energies produced with a frozen environment, but the values are often overshot. To ameliorate the problem, one needs to use wavefunction densities to polarize the environment. The choice of the exchange-correlation functional in the construction of the potential has little effect on the excitation, whereas the approximate kinetic-energy functional appears to be the largest source of error.