We present an overview of techniques designed for the reliable prediction of hyperfine interaction tensors in muonium-bearing radicals from Density Functional Theory (DFT). In general, the isotropic component is the most difficult to determine accurately. Anisotropic terms are often recovered satisfactorily at modest levels of theory. In small systems high-level electronic structure calculations may be used to demonstrate the importance of a number of key components in a successful treatment. The roles of basis set balance, electron correlation effects, and vibrational averaging over modes in which the muon is active are illustrated by calculations on a number of small inorganic and organic species. In larger systems DFT becomes the method of choice. However, the optimal choice of functional is not yet completely clear. Some cautionary tales are given along with some success stories.