Nucleic acids are essential biomolecules in living systems and represent one of the main targets of chemists, biophysics, biologists, and nanotechnologists. New small molecules are continuously developed to target the duplex (ds) structure of DNA and, most recently, RNA to be used as therapeutics and/or biological tools. Stimuli-triggered systems can promote and hamper the interaction to biomolecules through external stimuli such as light and metal coordination. In this work, we report on the interaction with ds-DNA and ds-RNA of two aza-macrocycles able to coordinate Zn2+ metal ions and form binuclear complexes. The interaction of the aza-macrocycles and the Zn2+ metal complexes with duplex DNA and RNA was studied using UV thermal and fluorescence indicator displacement assays in combination with theoretical studies. Both ligands show a high affinity for ds-DNA/RNA and selectivity for ds-RNA. The ability to interact with these duplexes is blocked upon Zn2+ coordination, which was confirmed by the low variation in the melting temperature and poor displacement of the fluorescent dye from the ds-DNA/RNA. Cell viability assays show a decrease in the cytotoxicity of the metal complexes in comparison with the free ligands, which can be associated with the observed binding to the nucleic acids.