The design and assembly of mechanically interlocked molecules, such as catenanes and rotaxanes, are dictated by various types of noncovalent interactions. In particular, [C-H center dot center dot center dot O] hydrogen-bonding and pi-pi stacking interactions in these supramolecular complexes have been identified as important noncovalent interactions. With this in mind, we examined the [3]catenane 2 center dot 4PF(6) using molecular mechanics (MM3), ab initio methods (HF, MP2), several versions of density functional theory (DFT) (B3LYP, M0X), and the dispersion-corrected method DFT-D3. Symmetry adapted perturbation theory (DFT-SAPT) provides the highest level of theory considered, and we use the DFT-SAPT results both to calibrate the other electronic structure methods, and the empirical potential MM3 force field that is often used to describe larger catenane and rotaxane structures where [C-H center dot center dot center dot O] hydrogen-bonding and pi-pi stacking interactions play a role. Our results indicate that the MM3 calculated complexation energies agree qualitatively with the energetic ordering from DFT-SAPT calculations with an aug-cc-pVTZ basis, both for structures dominated by [C-H center dot center dot center dot O] hydrogen-bonding and pi-pi stacking interactions. When the DFT-SAPT energies are decomposed into components, we find that electrostatic interactions dominate the [C-H center dot center dot center dot O] hydrogen-bonding interactions, while dispersion makes a significant contribution to pi-pi stacking. Another important conclusion is that DFT-D3 based on M06 or M06-2X provides interaction energies that are in near-quantitative agreement with DFT-SAPT. DFT results without the D3 correction have important differences compared to DFT-SAPT, while HF and even MP2 results are in poor agreement with DFT-SAPT.