The magnetic anisotropy of the supramolecular [2 x 2] grid [Co(II)(4)L-4](8+), with a bis(bipyridyl)-pyrimidine-based ligand L, was investigated by single-crystal magnetization measurements at low temperatures. The magnetization curves exhibit metamagnetic-like behavior and are explained by the weak-exchange limit of a minimal spin Hamiltonian including Heisenberg exchange, easy-axis ligand fields, and the Zeeman term. It is also shown that the magnetic coupling strength can be varied by the substituent R-1 in the two-position on the central pyrimidine group of the ligand L.