A focused library of newly designed monomeric and dimeric naphthalene diimides (NDIs) was analyzed in its ability to recognize specific G-quadruplex (G4) structures discriminating duplex DNA. The best G4 ligands—according to an affinity chromatography-based screening method named G4-CPG—were tested on human cancer and healthy cells, inducing DNA damage at telomeres, and in parallel, showing selective antiproliferative activity on HeLa cancer cells with IC50 values in the low nanomolar range. CD and fluorescence spectroscopy studies allowed detailed investigation of the interaction in solution with different G4 and duplex DNA models of the most promising NDI of the series, as determined by combining the biophysical and biological assays’ data.