Two novel copper(II) complexes of formulas {[Cu(4-Hmpz)4][Cu(4-Hmpz)2(µ3-ox-κ2O1,O2:κO2′:κO1′)(ClO4)2]}n (1) and {[Cu(3,4,5-Htmpz)4]2[Cu(3,4,5-Htmpz)2(µ3-ox-κ2O1,O2:κO2′:κO1′)(H2O)(ClO4)]2[Cu2(3,4,5-Htmpz)4(µ-ox-κ2O1,O2:κ2O2′,O1′)]}(ClO4)4·6H2O (2) have been obtained by using 4-methyl-1H-pyrazole (4-Hmpz) and 3,4,5-trimethyl-1H-pyrazole (3,4,5-Htmpz) as terminal ligands and oxalate (ox) as the polyatomic inverse coordination center. The crystal structure of 1 consists of perchlorate counteranions and cationic copper(II) chains with alternating bis(pyrazole)(µ3-κ2O1,O2:κO2′:κO1′-oxalato)copper(II) and tetrakis(pyrazole)copper(II) fragments. The crystal structure of 2 is made up of perchlorate counteranions and cationic centrosymmetric hexanuclear complexes where an inner tetrakis(pyrazole)(µ-κ2O1,O2:κ2O2′,O1′-oxalato)dicopper(II) entity and two outer mononuclear tetrakis(pyrazole)copper(II) units are linked through two mononuclear aquabis(pyrazole)(µ3-κ2O1,O2:κO2′:κO1′-oxalato)copper(II) units. The magnetic properties of 1 and 2 were investigated in the temperature range 2.0–300 K. Very weak intrachain antiferromagnetic interactions between the copper(II) ions through the µ3-ox-κ2O1,O2:κO2′:κO1′ center occur in 1 [J = −0.42(1) cm−1, the spin Hamiltonian being defined as H = −J∑S1,i · S2,i+1], whereas very weak intramolecular ferromagnetic [J = +0.28(2) cm−1] and strong antiferromagnetic [J’ = −348(2) cm−1] couplings coexist in 2 which are mediated by the µ3-ox-κ2O1,O2:κO2′:κO1′ and µ-ox-κ2O1,O2:κ2O2′,O1′ centers, respectively. The variation in the nature and magnitude of the magnetic coupling for this pair of oxalato-centered inverse copper(II) complexes is discussed in the light of their different structural features, and a comparison with related oxalato-centered inverse copper(II)-pyrazole systems from the literature is carried out.