The corannulene pincer (also known in the literature as the buckycatcher) is a fascinating system that may encapsulate, among other molecules, the C60 and C70 fullerenes. These complexes are held together by strong π-stacking interactions. Although these are quantum mechanical effects, their description by quantum chemical methods has proved very hard. We used three semi-empirical methods, PM6-D3H4X, PM6-D3H+ and GFN2-xTB, to model the interactions. Binding to fullerenes was extended to all open conformations of the buckycatcher, and with the proper choice of solvation model and partition functions, we obtained Gibbs free energies of binding that deviated by 1.0–1.5 kcal/mol from the experimental data. Adding three-body dispersion to PM6-D3H+ led to even better agreement. These results agree better with the experimental data than calculations using higher-level methods at a significantly lower fraction of the computational cost. Furthermore, the formation of adducts with C60 was studied using dynamical simulations, which helped to build a more complete picture of the behavior of the corannulene pincer with fullerenes. We also investigated the use of exchange-binding models to recover more information on this system in solution. Though the final Gibbs free energies in solution were worsened, gas-phase enthalpies and entropies better mirrored the experimental data.