A wide range of experimental, semiempirical, and theoretical values have been reported in the literature for the magnetic coupling parameters of the two-leg ladder compound SrCu2O3. We apply quantum chemical and density functional techniques to calculate accurate N-electron wave functions or densities for two different Cu2O7 clusters that represent the leg (Ji) and rung (J') of the ladder. Our data indicate that Ji is slightly larger than J' (J' /Ji'0.9) with J'52139 meV ~21670 K! and Ji52156 meV ~21870 K!. Recent experimental data indicate a more strongly anisotropic ratio, J' /Ji'0.5. The origin of the difference is unclear, as our ab initio estimates of J' and Ji seem to be converged with respect to the size of the basis set, the level of electron correlation, and the size of the cluster. However, we also find a surprisingly strong ferromagnetic interladder interaction which may play a role in resolving this discrepancy.