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We present a comprehensive analysis of magnetic coupling in a group of three popular chromium-based molecular rings, the homometallic Cr8ring and the heterometallic Cr7Ni and Cr7Zn molecules. We show conclusively that the broken symmetry approach within density functional theory (DFT), based on suitable conventional or range-separated hybrid functionals, provides a quantitatively reliable tool to extract magnetic exchange coupling parameters in all rings considered, which opens a window for additional applications in molecular magnetism. We further show that a nonempirical model spin Hamiltonian, based on the parameters extracted from DFT, leads to excellent agreement with experimental susceptibility data and energy spectra. Moreover, based on an optimally tuned range-separated hybrid functional approach, we find that gas-phase gaps of the studied molecular rings are much larger than previously calculated and discuss the implications of the revised electronic structure to potential applications in molecular spintronics.