Abstract: The fullerene-82 cavity is selected as a model system in order to test several methods for characterizing inclusion molecules. The methods are based on different technical foundations such as a square and triangular tessellation of the molecular surface, spherical tessellation of the molecular surface, numerical integration of the atomic volumes and surfaces, triangular tessellation of the molecular surface, and a cubic lattice approach the molecular volume. Accurate measures of the molecular volume and surface area have been performed with the pseudorandom Monte Carlo (MCVS) and uniform Monte Carlo (UMCVS) methods. These calculations serve as a reference for the rest of the methods. The SURMO2 method does not recognize the cavity and may not be convenient for intercalation compounds. The programs that detect the cavities never exceed 1-% deviation relative to the reference value for molecular volume and 5% for surface area. The GEPOL algorithm, alone or combined with TOPO, shows results in good agreement with those of the UMCVS reference. The uniform random number generator provides the fastest convergence for UMCVS and a correct estimate of the standard deviations. The effect of the internal cavity on the solvent-accessible surfaces has been calculated. Fullerene-82 is compared with fullerene-60 and -70.