The internal flexibility and interacting ability of PAMAM-dendrimers having 4-carbomethoxypyrrolidone-groups as surface groups (termed Gn-Pyr), which may be useful for biomedical purposes, and ion traps were investigated by analyzing the EPR spectra of their copper(II) complexes. Increasing amounts (with respect to the Pyr groups) of copper(II) gave rise to different signals constituting the EPR spectra at room and low temperature corresponding to different coordinations of Cu2+ inside and outside the dendrimers. At low Cu2+ concentrations, CuN4 coordination involving the DAB core is preferential for G3- and G5-Pyr, while G4-Pyr shows a CuN3O coordination. CuN2O2 coordination into the external dendrimer layer was also contributing to G3- and G4-Pyr spectra. The structures of the proposed copper-dendrimer complexes were also shown. G4-Pyr displays unusual binding ability toward Cu(II) ions. Mainly the remarkably low toxicity shown by G4-Pyr and its peculiar binding ability leads to a potential use in biomedical fields.