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A cutting-edge cancer treatment modality, that integrates MRI guidance and delivery of radiotherapy (MRIgRT), sets a new standard for personalised radiotherapy. There are, however, aspects around the accurate determination of absorbed dose in a magnetic field that need to be resolved. The influence of the Lorentz force on the secondary charged particles perturbs the detector dose response and this puts MRIgRT outside the scope of currently available protocols for reference dosimetry. The aim of this thesis is to investigate, clarify and resolve issues around traceable reference dosimetry for, and calibration of, MRIgRT systems. In this new context, I characterise the performance of suitable commercially available detectors in the presence of strong magnetic fields. Furthermore, potential routes to achieve traceability in dosimetry for MRIgRT, which are compatible with the existing standards and calibrations available for conventional radiotherapy, are identified and established. Finally, I propose guidelines for calibration and audit. In this thesis I show that Gafchromic EBT-3 film and alanine are suitable detectors for dosimetry, with the inclusion of appropriate corrections, in MRIgRT. Based on this finding and with the inclusion of alanine as reference class detector, I demonstrate a route for the calibration of secondary standard ionisation chambers in MRIgRT, in terms of absorbed dose to water traceable to the NPL (National Physical Laboratory) primary standard. This methodology is applied to the currently commercial and in the under-development of MRIgRT systems, and I show that the uncertainty is comparable to, if not quite matching, that of dosimetry for conventional radiotherapy. The application of work described in this thesis includes an alanine reference dosimetry service, for MRIgRT systems. This allows a dosimetry audit, provided by NPL, and the calibration of ionisation chambers (but also other dosimeters), either by a site visit to radiotherapy centres or as a postal dosimetry service.