Proteins bind fullerenes. Hydrophobic pockets can accommodate a carbon cage either in full or in part. However, the identification of proteins able to discriminate between different cages is an open issue. Prediction of candidates able to perform this function is desirable and is achieved with an inverse docking procedure that accurately accounts for (i) van der Waals interactions between the cage and the protein surface, (ii) desolvation free energy, (iii) shape complementarity, and (iv) minimization of the number of steric clashes through conformational variations. A set of more than 1000 protein structures is divided into four categories that either select C(60) or C(70) (p-C(60) or p-C(70)) and either accommodate the cages in the same pocket (homosaccic proteins, from σακκoζ meaning pocket) or in different pockets (heterosaccic proteins). In agreement with the experiments, the KcsA Potassium Channel is predicted to have one of the best performances for both cages. Possible ways to exploit the results and efficiently separate the two cages with proteins are also discussed.