Using dispersion-corrected DFT methods, an exhaustive computational study of all possible complexes between the carbon nanorings, CNRs, [10]CPP and [6]CPPA with the fullerenes C50 and C76 was carried out. For C50, the two more favorable isomers (with D5h and D3 symmetry) were chosen, and for C76, the isomer with D2 symmetry (the most favorable isomer of the two that exist) was the selected one. After exploration of all the possible rearrangements of the fullerenes inside the CNRs, optimization without any geometrical restrictions were carried out and the corresponding complexation energies were evaluated. According to calculations both CNRs can perform as satisfactory receptors of both fullerenes, what manifests through high complexation energies, going from − 36 to – 54 kcal mol−1. Almost in all complexes the fullerene stays fully inside the nanoring, except in the case of C76@[6]CPPA, where fullerene suffers a considerable departure of almost 2.5 A, which is certainly due to C76 to be too large for this CNR. Complexation of these systems is governed for the complementarity (of size and shape) between the CNR and the fullerene. While the fullerene is extremely rigid, the CNR has a certain capability to fit (in shape and size) to the fullerene, with the aim of optimizing the interaction between both monomers. This way, the CNR is able to contract slightly to embrace the host molecule more strongly.