The thermodynamic stability of 11 complexes of Cu(II) and 26 complexes of Fe(III) is studied, comprising the ligands pyridoxamine (PM), ascorbic acid (ASC), and a model Amadori compound (AMD). In addition, the secondary antioxidant activity of PM is analyzed when chelating both Cu(II) and Fe(III), relative to the rate constant of the first step of the Haber-Weiss cycle, in the presence of the superoxide radical anion (O2•−) or ascorbate (ASC−). Calculations are performed at the M05(SMD)/6-311+G(d,p) level of theory. The aqueous environment is modeled by making use of the SMD solvation method in all calculations. This level of theory accurately reproduces the experimental data available. When put in perspective with the stability of various complexes of aminoguanidine (AG) (which we have previously studied), the following stability trends can be found for the Cu(II) and Fe(III) complexes, respectively: ASC < AG < AMD < PM and AG < ASC < AMD < PM. The most stable complex of Cu(II) with PM (with two bidentate ligands) presents a ΔGf0 value of −35.8 kcal/mol, whereas the Fe(III) complex with the highest stability (with three bidentate ligands) possesses a ΔGf0 of −58.9 kcal/mol. These complexes can significantly reduce the rate constant of the first step of the Haber-Weiss cycle with both O2•− and ASC−. In the case of the copper-containing reaction, the rates are reduced up to 9.70 × 103 and 4.09 × 1013 times, respectively. With iron, the rates become 1.78 × 103 and 4.45 × 1015 times smaller, respectively. Thus, PM presents significant secondary antioxidant activity since it is able to inhibit the production of ·OH radicals. This work concludes a series of studies on secondary antioxidant activity and allows potentially new glycation inhibitors to be investigated and compared relative to both PM and AG.