Hyperfine parameters obtained from experimental techniques such as electron paramagnetic resonance contain a wealth of information about defects in semiconductors. Detailed structural information can only be extracted, however, if accurate calculations are available with which the experimental quantities can be compared. We show that reliable values for hyperfine parameters can be obtained from first-principles calculations based on spin-density-functional theory and pseudopotentials. We present a method that overcomes the complication that the wave functions in the core region are not directly available in a pseudopotential formalism. The power of the approach will be illustrated with examples for a number of different defect systems, including H in various semiconductors (Si, GaAs, and ZnSe), and the Zn interstitial in ZnSe.