In this study, we present calculations of the circular dichroism (CD) spectra of complexes between achiral and chiral molecules. Nonzero rotational strengths for transitions of the nonchiral molecule are induced by interactions between the two molecules, which cause electronic and/or structural perturbations of the achiral molecule. We investigate if the chiral molecule (environment) can be represented only in terms of its frozen electron density, which is used to generate an effective embedding potential. The accuracy of these calculations is assessed in comparison to full supermolecular calculations. We can show that electronic effects arising from specific interactions between the two subsystems can reliably be modeled by the frozen-density representation of the chiral molecule. This is demonstrated for complexes of 2-benzoylbenzoic acid with (-)-(R)-amphetamine and for a nonchiral, artificial amino acid receptor system consisting of ferrocenecarboxylic acid bound to a crown ether, for which a complex with L-leucine is studied. Especially in the latter case, where multiple binding sites and interactions between receptor and target molecule exist, the frozen-density results compare very well with the full supermolecular calculation. We also study systems in which a cyclodextrin cavity serves as a chiral host system for a small, achiral molecule. Problems arise in that case because of the importance of excitonic couplings with excitations in the host system. The frozen-density embedding cannot describe such couplings but can only capture the direct effect of the host electron density on the electronic structure of the guest. If couplings play a role, frozen-density embedding can at best only partially describe the induced circular dichroism. To illustrate this problem, we finally construct a case in which excitonic coupling effects are much stronger than direct interactions of the subsystem densities. The frozen density embedding is then completely unsuitable.