AbstractBy means of density functional calculations, we studied the performance of 2 fullerene receptors that contain 3 corannulene or triphenylene pincers. For the first time, we found a receptor that has a small tendency to form intramolecular stacks between the 3 corannulene pincers. After comparing their ability to trap fullerenes, with that of buckycatcher, buckycatcher‐II, and the Venus flytrap, we conclude that a record‐breaking association constant is expected for the receptor with 3 corannulene pincers. Although triphenylene is less effective than the corannulene units in forming inclusion complexes with C60, the triphenylene‐based host is also expected to have a high association constant. Finally, we discuss the theoretical problems found in reproducing the experimental free energy changes in solution for buckycatcher, buckycatcher‐II, and the Venus flytrap.