In this work, we report the synthesis and characterization of three novel copper(II) complexes of naphthyl derived 3-hydroxy-4-pyridinone chelators. Their antibacterial activity against several Gram-positive and Gram-negative reference strains and multidrug-resistant clinical isolates was assessed through determination of the minimum inhibitory concentration (MIC). The complex Cu(naph1pp)2 shows the highest antibacterial activity, including against multidrug-resistant isolates, nonetheless, being more active against Gram-positive than Gram-negative bacteria. Cu(naph1pp)2 was further explored in combinatorial tests with ciprofloxacin against methicillin-resistant Staphylococcus aureus (MRSA) and vancomycin-resistant Enterococcus faecalis (VRE). The combination of Cu(naph1pp)2 and ciprofloxacin is considered additive, i.e., the effect of the two compounds combined is stronger than that of the individual compounds in the equivalent concentration.