Stability constant values and bonding details of the copper(II) complexes of the β-cyclodextrin functionalized with the carnosine dipeptide (β-alanyl-L-histidine) at its narrow (CDAH6) or at its wide (CDAH3) rim were determined in aqueous solution. The potentiometric and spectroscopic data (UV-vis, CD and EPR) show that the involvement of a secondary OH group induces drastic differences in the coordination properties of CDAH3, in comparison with those of CDAH6. Direct and indirect assays were carried out showing that the copper(II) complexes with the two cyclodextrin derivatives are SOD-mimics with high catalytic activity. In addition the complex species are scavenger compounds towards ˙OH radicals, giving rise to a particular kind of copper(II) complexes with a combined activity against two toxic radical species, O2˙− and ˙OH. The cyclodextrin moiety contributes to the scavenger activity, without damaging the cellular membranes of neuronal and red blood cells.