Reactions between N6O4 macrocyclic 1,4,19,22,25,40-hexaaza-10,13,31,34-tetraoxa-6,14,27,35(1,4)-tetrabenzenacyclopentacontane (L) and several copper salts (viz. trifuoromethane and toluene sulfonates, nitrate, perchlorate, benzoate, and acetate) led to the formation of dinuclear compounds [Cu2(OSO2CF3)2(DMF)2L](SO3CF3)2 (1), [Cu2(p-OSO2C6H4Me)2L(DMF)2](SO3C6H4Me)2 (2), [Cu2(ONO2)2L(DMF)2](NO3)2 (3), [Cu2(OClO3)2(DMF)2L](ClO4)2 (4), [Cu2(OOCPh)2L(H2O)2](O2CPh)2 (5), and [Cu2(OOCMe)4L] (6), which were characterized by IR, elemental analysis and TG-DTA (thermogravimetric-differential thermal analysis), as well as by single-crystal X-ray diffraction, EPR (electron paramagnetic resonance) spectroscopy, and electrochemical techniques (cyclic voltammetry and controlled potential electrolysis). The molecular structures of compounds 1–6 reveal a considerable conformational flexibility of the ligand L, which allowed its readjustment for the formation of the metal compounds and confirmed the presence of dinuclear endo macrocyclic species. In every case, the L ligand coordinates to each copper cation via three nitrogen atoms, with the remaining coordination positions of the metal square pyramid environment being accomplished by neutral or anionic ligands. The macrocyclic cavities appear to be adequate for the enclosure of a neutral species as proved by compound 6 with 1,4-dioxane. The compounds, in combination with the TEMPO (2,2,6,6-tetramethyl-piperidinyloxyl) radical and in alkaline aqueous solution, act as efficient catalysts in the aerobic oxidation of different alcohols to the corresponding aldehydes (yields up to 99% and TON up 232) after 20 h at 70 °C. In addition, the microwave-assisted solvent-free peroxidative oxidation (by tert-butylhydroperoxide, TBHP) of 1-phenylethanol led to acetophenone yields up to 99% and TOF of 1.1 × 103 after 0.5 h, without any additive.