A series of buckybowls with different sizes and structures have been tested as potential receptors of fullerenes C60, C70 and C40. Among these bowls are corannulene (C20H10), sumanene (C21H12), pinakene (C28H14), hemifullerene (C30H12), circumtrindene (C36H12), pentaindenocorannulene (C50H20) and bowl-shaped hexabenzocoronene derivatives. An exhaustive study, taking into account different orientations of fullerenes, was performed in order to obtain the most favourable arrangement for interacting with the bowls. Complexes were optimised at the SCC-DFTB-D level and interaction energies were obtained at the B97-D2/TZVP level including BSSE corrections. Comparison with the full B97-D2/TZVP results (optimisation plus interaction energies) suggests that the B97-D2/TZVP//SCC-DFTB-D approach may be a useful screening tool for designing fullerene receptors. Regarding the "catching" ability of the different buckybowls, it can be concluded that the shape of a buckybowl plays a crucial role in its success. Thus, it seems that the addition of flaps at the bowl rim by benzannelation is an effective strategy for enhancing the interaction with fullerenes, providing enough flexibility to extend the contact surface with the fullerene moiety. Accordingly, a bowl-shaped hexabenzocoronene derivative (C72H24) showed the best ability among the buckybowls evaluated for catching the fullerenes C60, C70 and C40; it is noteworthy that, when interacting with C60, the interaction energy is three times that corresponding to the prototypical buckybowl, corannulene. On the contrary, the more rigid and compact is the structure of a buckybowl, the smaller its ability to interact with fullerenes.