A microporous copper(II) carboxylate complex, copper(II) trans-1,4-cyclohexanedicarboxylate [Cu₂^II,II(OOCC₆H₁₀COO)₂]·H₂O (1) can act as a biomimetic heterogeneous catalyst for selective oxidation of various alcohols with H₂O₂. A green-colored active intermediate, H₂[Cu₂^II,II(OOCC₆H₁₀COO)₂(O₂)]·H₂O (2), observed in the reaction of 1 with 20-fold excess H₂O₂ in acetonitrile was characterized by elemental analysis, TG/DTA, magnetic susceptibility, FT-IR, diffuse reflectance (DR) UV-vis, electron paramagnetic resonance (EPR), X-ray powder diffraction (XRPD), resonance Raman, BET surface area, pore size distribution, and nitrogen occlusion measurements. The molecular structure of 2 was determined from XRPD data and refined by the Rietveld method. The microporous structure of 2 was constructed by intermolecular bridging of μ-1,2-trans Cu-OO-Cu species between two-dimensional [Cu₂(O₂CC₆H₁₀CO₂)] layers, which was the first example of microporous copper(II) peroxo complex for heterogeneous oxidation catalysis. Moreover, a microporous ruthenium(II,III) complex having porphyrin [Ru^II,III₂(H₂TCPP)]BF₄ (3) (H₂TCPP=4,4',4",4 -(21H,23H-porphine-5,10,15,20-tetrayl)tetrakis benzoic acid) particularly exhibited an effective catalytic performance for the heterogeneous oxidation of primary aliphatic alcohols with dioxygen and air without any additives at room temperature. The reaction pathway included the formation of an Ru-oxygen radical intermediate, which was due to the high affinity of diruthenium(II,III) sites for dioxygen.