The specific properties of carbon-based nanomaterials like fullerenes and graphenes have attracted a continuous interest for their possible use as drug carriers. The functionalization of these nanomaterials can lead to the variation or improvement of the required properties, in order to lead to the design of the most suitable compounds within a specific field. In this regard, the possible use of a new class of nanostructures -the rhombellanes- as nanocarriers is investigated. The aim of the paper is to study the interactions of indomethacin and four analogues with anti-inflammatory activity on 13 rhombellanes (three of them with a hyper-adamantane motif, Ada-rbl, three cube-rhombellane homeomorphs, C-rbl, and seven cube-rhombellane-ether/amine structures). Five compounds with anti-inflammatory activity have been docked to the surface of the rhombellanes; comparisons with the results obtained for fullerene C60 have been performed. The best binding affinities for the indomethacin and its derivatives have been obtained for two types of rhombellanes, Ada-rbl and C-rbl. The indomethacin analogue I4 shows an increased binding affinity for C-rbl.420, similar to the value obtained for C60. Best results have been obtained for rhombellane derivatives characterized by smaller HOMO-LUMO gaps.