The preparation, X-ray crystal structure, spectroscopic and variable-temperature dc and ac magnetic properties of two six-coordinate cobalt(ii) complexes of formula [Co(bim)4(tcm)2] (1) and [Co(bmim)4(tcm)2] (2) (bim = 1-benzylimidazole, bmim = 1-benzyl-2-methylbenzimidazole and tcm- = tricyanomethanide ion) are reported. 1 and 2 crystallize in the monoclinic P21/n and C2/c space groups with the asymmetric units composed of one tcm- ion and half the [Co(bim)4]2+ and [Co(bmim)4]2+ complex cations, respectively. Their cobalt atoms are in compressed (1)/rhombic (2) CoN6 octahedral environments, the axial positions being occupied by monodentate tricyanomethanide anions. The neutral molecules in 1 are linked through weak C-HN type interactions into supramolecular chains, which are further interconnected into supramolecular 2D motifs by C-Hπ stacking. No short intermolecular interactions occur in 2. The values of the shortest intermolecular cobalt-cobalt separation are 10.901(1) (1) and 10.577(3) Å (2). Detailed ac and dc magnetic studies indicate that 1 and 2 are field-induced single-ion magnets (SIMs) with D = +46.1 (1)/+80.1 cm-1 (2) thus presenting new examples of SIMs with transversal magnetic anisotropy. Theoretical calculations by CASSCF/NEVPT2 support these results and suggest that the relaxation of the magnetization occurs in the ground state under applied fields through two Orbach processes possibly bound to low-lying vibrational modes. Q-band EPR study for polycrystalline samples 1 and 2 at low temperatures confirms the positive sign of D, allows the rough estimation of the E/D ratio [0.144 (1) and 0.180 (2)] and reveals the occurrence of a strong asymmetry in the g-tensors. The values found for the spin-reversal barrier, Ea ≈ 28 and 11 cm-1 (1) and 20 and 9 cm-1 (2), are within the range of those found in other cobalt(ii) field-induced SIMs with a pseudooctahedral trans-CoN4N'2 chromophore.