Two mononuclear cobalt(II) compounds of formula [Co(dmphen)(2)(OOCPh)]ClO4 center dot 1/2H(2)O center dot 1/2CH(3)OH (1) and [Co(dmbipy)(2)(OOCPh)]ClO4 (2) (dmphen = 2,9-dimethyl-1,10-phenanthroline, dmbipy = 6,6'-dimethyl-2,2'-bipyridine and HOOCPh = benzoic acid) are prepared and magnetostructurally investigated. Each cobalt(II) ion is six-coordinate with a distorted octahedral CoN4O2 environment. The complex cations are interlinked leading to supramolecular chains (1) and pairs (2) that grow along the crystallographic c-axis with racemic mixtures of (Delta,Lambda)-Co units. FIRMS allowed us to directly measure the zero-field splitting between the two lowest Kramers doublets, which led to axial anisotropy values of 58.3 cm(-1) <= D < 60.7 cm(-1) (1) and 63.8 cm(-1) <= D < 64.1 cm(-1) (2). HFEPR spectra of polycrystalline samples of 1 and 2 at low temperatures confirm the positive sign of D and provide an estimate of the E/D quotient [0.147/0.187 (1) and 0.052 (2)]. Detailed ac and dc magnetic studies reveal that 1 and 2 are new examples of field-induced single-ion magnets (SIMs) with small transversal anisotropy. CASSCF/NEVPT2 calculations support these results. Two Orbach processes or one Orbach plus a direct relaxation mechanism provide similar agreements with the nonlinear experimental Arrhenius plots at H-dc = 500 and 2500 G for 1. Two independent relaxation processes occur in 2, but in contrast to 1, an observed linear dependence of ln(tau) vs 1/T substantiates Orbach processes against the most widely proposed Raman and direct mechanisms. The analysis of each relaxation process in 2 provided values for Ea and To that are very close to those found for 1, validating the predominant role of the Orbach relaxations in both compounds and, probably, also in other cobalt(II) SIMs. A mechanism based on a spin-phonon coupling is proposed to account for the SIM behavior in 1 and 2 with any Raman or direct processes being discarded.