The potential stabilization of normally unstable C-20, the smallest fullerene, via its encapsulation inside a tetraureacalix[4]arene dimer has been analyzed using molecular mechanics calculations with different force fields, the self-consistent-charge density-functional tight-binding with dispersion correction (SCC-DFTB-D) model, and standard density-functional-theory (DFT) calculations. The interaction energies obtained for the C-20 complex have been compared with analogous values calculated for numerous complexes of the tetraureacalix[4]arene dimer with other guests. Results of the calculations with all force fields and SCC-DFTB-D predict that the binding of C-20 occurs with the highest selectivity. On the other hand, standard DFT calculations fail to correctly describe the stabilization of the complexes under study as standard DFT generally does not treat dispersion interactions properly. Predicted relative stabilities of the complexes are discussed in conjunction with available experimental data. Molecular dynamics simulations reveal the instability of the guest-free capsular dimer, which decomposes on a 1-ns time scale, while dimeric complexes with guests remained intact during the 5-ns simulation time, indicating the guest-driven formation of the molecular capsule.