Copper(I)-catalyzed azide-alkyne cycloaddition was employed to construct biscalixarene assemblies from the calix[4]arene dipropargyl ethers and 4,4′-bis-azidomethylated azobenzene or stilbene. Three bis(calixarenes) having the calix[4]arene cores linked to each other by pairs of (E)-azobenzene/stilbene units through four triazole groups were obtained as confirmed by NMR, HRMS and X-ray diffraction data. Nevertheless, the formation of larger macrocycles and polymeric/oligomeric products was found to be the major competing process that seriously limited the applicability of the one-step macrocyclization approach for the construction of photoresponsive biscalixarene assemblies linked by pairs of azobenzene/stilbene units.