The preparations of related mononuclear and binuclear Co(II) complexes with a quasi-identical local C3v symmetry using a cryptand organic ligand are reported. The mononuclear complex behaves as a single molecule magnet (SMM). A relatively weak antiferromagnetic exchange coupling (J) of the same order of magnitude as the local magnetic anisotropy (D) is determined experimentally and theoretically for the binuclear complex. The weak magnitude of the antiferromagnetic exchange coupling, analyzed using a combination of broken-symmetry density functional theory and wave function based calculations, is ascribed to the weak overlap between the singly occupied orbitals because of the local C3v symmetry of the Co(II) ions; the organic ligand was found to contribute to the exchange coupling as the azido bridge that directly links the Co(II) ions. Calculation of the energy and wave functions of the spin states for the binuclear complex, in the general case, allows analysis of the effect of the |J/D| ratio on the magnetic behavior of the binuclear complex and prediction of the optimum range of values for the complex to behave as two weakly interacting SMMs.