This dissertation deals with electromagnetic field modelling and performance simulation of a synchronous generator with a high temperature superconducting rotor. The work presented in this thesis covers detailed modelling of magnetic field distributions and optimisation undertaken in parallel with the design and manufacturing. The design of the generator is a very complex process involving electromagnetic, mechanical and thermal aspects, thus thorough understanding of the technology is very important. Hence, the first part of this thesis gives an introduction to superconductivity including layout of the most advanced high temperature superconducting materials and the state-of-the-art in the most recent designs of electric power devices using superconductors. The superconducting tape's characteristics that are necessary for the generator design and modelling are described. The selection of the rotor core material is also discussed from the point of view of very low temperature environment. The OPERA finite-element software package is used to model various rotor designs. Three electromagnetic issues were identified as of particular importance in this design: shaping of the magnetic Held in the region of the superconducting tapes to reduce the field perpendicular to the broad face of the tape, harmonic content in the voltage waveform and reduction of losses released in the cold region. The undesirable harmonics of the output voltage, which tend to circulate harmonic currents in the stator winding and the external circuit, are identified and minimised where possible, and the prediction results are compared to those obtained from measurement. Furthermore, finite-element analysis was employed to evaluate the critical parameters such as reactances and time constants required for future stability studies. A possible design and structure of the next generation synchronous generator with a HTS coreless rotor are briefly discussed based on the current design.