Two hexacoordinate Co(II) complexes [Co(hfac)2(etpy)2] (1) and [Co(hfac)2(bzpyCl)2] (2) were synthesized and spectrally and structurally characterized. The {CoO4N2} chromophore adopts a geometry of the elongated tetragonal bipyramid with a small o-rhombic component. This less common arrangement causes the magnetic data to need be analysed using the Griffith-Figgis model, instead of the commonly used spin-Hamiltonian with zero-field splitting parameters D and E. In the case of the elongated bipyramid for d7 complexes, the source of the magnetic anisotropy of an easy-axis type is the axial crystal field splitting Δax. The ab initio CASSCF calculations followed by the NEVPT2 module confirm that the ground electronic term is quasi-degenerate owing to the splitting of the 4Eg (D4h) mother term. The lowest spin-orbit multiplets appear as four Kramers doublets belonging to the Γ5 irreducible representation of the double point group D2'. They exhibit a serious mixing of the |±1/2〉 and |±3/2〉 spins which reflects a sizable effect of the spin-orbit coupling. Both complexes exhibit field-supported slow magnetic relaxation governed by the Raman process.