The reaction of the Schiff base (3,5-di-tert-butyl-2-hydroxybenzylidene)-2-hydroxybenzohydrazide (H3L) with a copper(II) salt of a base of a strong acid, i.e., nitrate, chloride or sulphate, yielded the mononuclear complexes [Cu(H2L)(NO3)(H2O)] (1), [Cu(H2L)Cl]·2MeOH (2) and the binuclear complex [{Cu(H2L)}2(µ-SO4)]·2MeOH (3), respectively, with H2L− in the keto form. Compounds 1–3 were characterized by elemental analysis, Infrared (IR) spectroscopy, Electrospray Ionisation Mass Spectrometry (ESI-MS) and single crystal X-ray crystallography. All compounds act as efficient catalysts towards the peroxidative oxidation of cyclohexane to cyclohexyl hydroperoxide, cyclohexanol and cyclohexanone, under mild conditions. In the presence of an acid promoter, overall yields (based on the alkane) up to 25% and a turnover number (TON) of 250 (TOF of 42 h−1) after 6 h, were achieved.