High Temperature Superconductor (HTS) magnets are enabling components for many valuable applications including medical imaging and fundamental physics research. One major inconvenience of using superconducting components is the need to cool them to a very low temperature, and once at this low temperature, to power them. This requires the use of cryogenic systems and power supplies, which are often larger and more complex than the superconducting components. The aim of the work in this thesis is to develop better and more flexible power supplies for superconducting magnets, known as flux pumps. These devices power superconducting magnets wirelessly, isolating the power supply from the magnet both thermally and mechanically. This reduces the power requirement for keeping the magnet cold, cutting both power consumption and the size and weight of the cryogenic system. This thesis focusses specifically on developing improved HTS flux pumps of the transformer-rectifier type and seeks to demonstrate their feasibility and advantage over conventional technology. First, new simulation models are presented which help to understand transformer-rectifier flux pumps and how to optimise them. Based on analysis of these models, superconducting switches are the most important components of these devices. The subsequent section documents the development of an improved superconducting power switch, which shows a tenfold increase in performance compared to switches of this type previously reported on. These switches were used to build a transformer-rectifier flux pump which provides 100 mV to a load magnet, the highest output voltage for an HTS flux pump to date. Based on work from previous chapters, a design methodology for transformer-rectifier flux pumps is presented, giving examples of future designs and their trade-offs. Finally, the current state of flux pump technology is discussed, concluding that that flux pumps are a compelling technology and that future work should focus on demonstrating flux pumps in applications.