Due to its associated low CO2 emissions, nuclear energy production is rapidly growing. In this context, the treatment of high-level liquid waste (HLLW) of nuclear plants is of high concern to both scientific and industrial communities. Specifically, the separation of An(III) and Ln(III) cations when processing nuclear fuel is a vitally important, yet challenging, step within HLLW because An(III) and Ln(III) have similar chemical properties in solution. To guide the choice of relevant ligands, anions, and solvents for this separation step, in this work, we calculate and compare the free energy of formation of different Am(III) and Eu(III) complexes (which are typical and important An(III) and Ln(III) cation examples), involving two different ligands and three different counter ions in four different solvents. Based on our calculations, we predict that the chosen solvent is a key factor in the extraction of Am(III) and Eu(III) in treatment of HLLW. This study supports a systematic, computation-assisted screening of solvents and extractive ligands with counter anions as a proficient method to optimize the separation of Ln(III) and An(III).