Nuclear magnetic resonance (NMR) is a popular spectroscopic method and has widespread use in many fields. Recent developments in solid-state NMR have increased interest in experiment and, alongside simultaneous developments in computational theory, have led to the field dubbed 'NMR crystallography.' This is a suite of methodologies, complementing the capabilities of other crystallographic methods in the determination of atomic structure, especially when large crystals cannot be made and when exploring materials with phenomena such as compositional, positional and dynamic disorder. NMR J-coupling is the indirect coupling between nuclear spins, which, when measured, can reveal a wealth of information about structure and bonding. This thesis develops and applies the method of Joyce for the prediction of NMR J-coupling in condensed matter systems using plane-wave pseudopotential density-functional theory, an important requirement for efficient treatment of finite and infinite periodic systems. It describes the first-ever method for the use of ultrasoft pseudopotentials and inclusion of special relativistic effects in J-coupling prediction, allowing for the treatment of a wider range of materials systems and overall greater user friendliness, thus making the method more accessible and attractive to the wider scientific community.