We report single-crystal X-band EPR and magnetic measurements of the coordination polymer catena-(trans-(mu(2)-fumarato)tetraaquacobalt(II)), 1, and the Co(II)-doped Zn(II) analogue, 2, in different Zn:Co ratios. 1 presents two magnetically inequivalent high spin S = 3/2 Co(II) ions per unit cell, named A and B, in a distorted octahedral environment coordinated to four water oxygen atoms and trans coordinated to two carboxylic oxygen atoms from the fumarate anions, in which the Co(II) ions are linked by hydrogen bonds and fumarate molecules. Magnetic susceptibility and magnetization measurements of 1 indicate weak antiferromagnetic exchange interactions between the S = 3/2 spins of the Co(II) ions in the crystal lattice. Oriented single crystal EPR experiments of 1 and 2 were used to evaluate the molecular g-tensor and the different exchange coupling constants between the Co(II) ions, assuming an effective spin S' = 1/2. Unexpectedly, the eigenvectors of the molecular g-tensor were not lying along any preferential bond direction, indicating that, in high spin Co(II) ions in roughly octahedral geometry with approximately axial EPR signals, the presence of molecular pseudo axes in the metal site does not determine preferential directions for the molecular g-tensor. The EPR experiment and magnetic measurements, together with a theoretical analysis relating the coupling constants obtained from both techniques, allowed us to evaluate selectively the exchange coupling constant associated with hydrogen bonds that connect magnetically inequivalent Co(II) ions (IJ(AB)(1/2)vertical bar = 0.055(2) cm(-1)) and the exchange coupling constant associated with a fumarate bridge connecting equivalent Co(II) ions (IJ(AA)(1/2)vertical bar approximate to 0.25 (1) cm(-1)), in good agreement with the average J(3/2) value determined from magnetic measurements.