Magnetic exchange-coupling constants of tri- and dinuclear transition-metal complexes (paddlewheels) have been computed using various ab initio methods. The di- and trinuclear complexes under study may serve as secondary building units in metal-organic frameworks (MOFs). Multi-reference methods such as the complete-active-space self-consistent-field method (CASSCF) as well as second-order perturbation theory (CASPT2) yield spin ladders from which the magnetic exchange-coupling constants are obtained. For the dicobalt paddlewheels, inclusion of spin-orbit coupling is crucial for obtaining a qualitatively correct description of the system. Density functional theory (DFT) was applied in the framework of the broken-symmetry approach using single- and double-hybrid functionals as well as generalized-gradient-approximation (GGA) functionals. The computed magnetic exchange-coupling constants are compared with experimental and other theoretical data, where available.