Quantum-mechanical embedding methods have in recent years gained significant interest and may now be applied to predict a wide range of molecular properties calculated at different levels of theory. To reach a high level of accuracy in embedding methods, both the electronic structure model of the active region and the embedding potential need to be of sufficiently high quality. In fact, failures in quantum mechanics/molecular mechanics (QM/MM)-based embedding methods have often been associated with the QM/MM methodology itself; however, in many cases the reason for such failures is due to the use of an inaccurate embedding potential. In this paper, we investigate in detail the quality of the electronic component of embedding potentials designed for calculations on protein biostructures. We show that very accurate explicitly polarizable embedding potentials may be efficiently designed using fragmentation strategies combined with single-fragment ab initio calculations. In fact, due to the self-interaction error in Kohn-Sham density functional theory (KS-DFT), use of large full-structure quantum-mechanical calculations based on conventional (hybrid) functionals leads to less accurate embedding potentials than fragment-based approaches. We also find that standard protein force fields yield poor embedding potentials, and it is therefore not advisable to use such force fields in general QM/MM-type calculations of molecular properties other than energies and structures.