A series of monocapped cobalt(II) tris-pyrazoloximates was obtained through the template condensation of the corresponding pyrazoloxime, phenylboronic acid and a suitable cobalt(II) halogenide. Comparing 3-acetylpyrazoloxime versus its methine-containing homolog, the former produced cobalt(II) clathrochelates in substantially higher yields due to the electron donating effect of the methyl substituent, increasing the N-donor ability of its oxime group. Their less N-donor analog with the electron acceptor trifluoromethyl group did not form cobalt(II) complexes of this type. In all their solvent-free and solvent-containing crystals, the encapsulated cobalt(II) ion adopted a high-spin state, as gauged by the Co-N bond lengths of 2.112(4)-2.188(9) Å, and was located almost in the center of its CoN6-coordination polyhedron. Their CoN6-polyhedra had an almost ideal trigonal-prismatic (TP) geometry with distortion angles φ below 4°. This TP-like geometry was assisted by hydrogen bonding between their NH groups and the apical counterion. The absence of methyl groups makes them close to an ideal TP. In contrast, stronger N-H⋯Cl hydrogen bonds occurred in the methyl-containing complex, while the Co-N bond lengths stayed the same at 2.144(2) Å on average. In its solvates with benzene, chloroform and acetone, there is a clear tendency for φ to decrease from 2.7(3)° to 0.47(13)°. The comparable effects of the ribbed methyl substituents, the cross-linking counterion and the lattice solvent on their molecular geometry were observed; the larger the distortions from an ideal TP geometry, the stronger the hydrogen bonds to the corresponding apical halogenide anion. The analysis of the experimental AC- and DC-magnetometry data for their fine-crystalline samples suggests that the passing from the derivative of the methyl-substituted synthon to that of its methine-containing homolog caused a substantial decrease in the magnetic susceptibility value χT and an increase in the QTM contribution to the magnetic relaxation. The effect of a cross-linking halogenide counteranion on the Orbach remagnetization barrier is greater than that of the solvatomorphism of their crystals.