State of the art CASSCF and CASPT2 calculations have been performed to elucidate the nature of ferromagnetism of CoII-NC-WV pairs in the three-dimensional compound [[WV(CN)2]2[(micro-CN)4CoII(H2O)2]3.4H2O]n, which has been recently synthesized and investigated by a number of experimental techniques (Herrera, J. M.; Bleuzen, A.; Dromzée, Y.; Julve, M.; Lloret, F.; Verdaguer, M. Inorg. Chem. 2003, 42, 7052-7059). In this network, the Co ions are in the high-spin (S = 3/2) state, while the single unpaired electron on the W centers occupies the lowest orbital of the dz2 type of the 5d shell. In agreement with the suggestion made by Herrera et al., we find that the ferromagnetism is due to a certain occupation scheme of the orbitals from the parent octahedral t2g shell on CoII sites, in which the orbital accommodating the unpaired electron is orthogonal to the dz2 orbitals of the surrounding W ions. We investigate the stabilization of such an orbital configuration on the Co sites and find that it cannot be achieved in the ground state of isolated mononuclear fragments [CoII(NC)4(OH2)2]2- for any conformations of the coordinated water molecules and Co-N-C bond angles. On the other hand, it is stabilized by the interaction of the complex with neighboring W ions, which are simulated here by effective potentials. The calculated exchange coupling constants for the CoII-NC-WV binuclear fragments are in reasonable agreement with the measured Curie-Weiss constant for this compound. As additional evidence for the inferred electronic configuration on the Co sites, the ligand-field transitions, the temperature-dependent magnetic susceptibility, and the field-dependent low-temperature magnetization, simulated ab initio for the mononuclear Co fragments, are in agreement with the available data for another compound [WIV[(micro-CN)4-CoII(H2O)2]2.4H2O]n containing diamagnetic W and high-spin Co ions in an isostructural environment.