Density functional theory calculations have been used to explore the potential of Ru-based complexes with 1,3-bis(2,4,6-trimethylphenyl)imidazolin-2-ylidene (SIMes) ligand backbone (A) being modified in silico by the insertion of a C60 molecule (B and C), as olefin metathesis catalysts. To this end, we investigated the olefin metathesis reaction catalyzed by complexes A, B, and C using ethylene as the substrate, focusing mainly on the thermodynamic stability of all possible reaction intermediates. Our results suggest that complex B bearing an electron-withdrawing N-heterocyclic carbene improves the performance of unannulated complex A. The efficiency of complex B is only surpassed by complex A when the backbone of the N-heterocyclic carbene of complex A is substituted by two amino groups. The particular performance of complexes B and C has to be attributed to electronic factors, that is, the electronic-donating capacity of modified SIMes ligand rather than steric effects, because the latter are predicted to be almost identical for complexes B and C when compared to those of A. Overall, this study indicates that such Ru-based complexes B and C might have the potential to be effective olefin metathesis catalysts.