Exchange coupling parameters and isotropic Mn-55 hyperfine couplings of fourteen mixed-valence Mn(III)-Mn(IV) dimers are determined using broken-symmetry density functional theory (DFT) and spin projection techniques. A systematic evaluation of density functional approaches shows that the TPSSh functional yields the best exchange coupling constants among all investigated methods, with deviations from experiment of the order of similar to 10-15%. For the prediction of Mn-55 hyperfine couplings the deficiencies of DFT in the description of core-level spin-polarization and the neglect of scalar relativistic effects lead to systematic deviations between theory and experiment that can be compensated through the use of a universal scaling factor. We determine this scaling factor to be 1.49 and demonstrate that the Mn-55 hyperfine couplings in mixed-valence Mn(Ill,IV) dimers can be successfully and systematically predicted with the TPSSh functional and the proposed spin projection techniques. The dependence of isotropic Mn-55 hyperfine couplings on the Mn(III) zero-field splitting values is studied in detail using a dimer for which the strong exchange approximation breaks down, In this case we apply a rigorous form of our spin projection technique that incorporates zero-field splitting contributions to the site spin expectation values. These results form the basis for future studies that aim at deducing unknown structures on the basis of computed spectroscopic parameters.