A former spectroscopic study of Cu(II) coordination by the 13-membered ring cyclic tetrapeptide c(Lys-dHis-βAla-His) (DK13), revealed the presence, at alkaline pH, of a stable peptide/Cu(III) complex formed in solution by atmospheric dioxygen oxidation. To understand the nature of this coordination compound and to investigate the role of the His residues in the Cu(III) species formation, Cu K-edge XANES, and EXAFS spectra have been collected for DK13 and two other 13-membered cyclo-peptides: the diastereoisomer c(Lys-His-βAla-His) (LK13), and c(Gly-βAla-Gly-Lys) (GK13), devoid of His residues. Comparison of pre-edge peak features with those of Cu model compounds, allowed us to get information on copper oxidation state in two of the three peptides, DK13 and GK13: DK13 contains only Cu(III) ions in the experimental conditions, while GK13 binds only with Cu(II). For LK13/Cu complex, EXAFS spectrum suggested and UV-vis analysis confirmed the presence of a mixture of Cu(II) and Cu(III) coordinated species. Theoretical XANES spectra have been calculated by means of the MXAN code. The good agreement between theoretical and experimental XANES data collected for DK13, suggests that the refined structure, at least in the first coordination shell around Cu, is a good approximation of the DK13/Cu(III) coordination species present at strongly alkaline pH. All the data are consistent with a slightly distorted pyramidal CuN(4) unit, coming from the peptide bonds. Surprisingly, the His side-chains seemed not involved in the final, stable, Cu(III) scaffold.