Permanent magnets are essential components for many devices such as motors, which currently account for 45 % of global electricity consumption, generators and also superconducting magnetic bearings used for applications such as flywheel energy storage. But even the most powerful rare-earth magnets are limited to a remanent field of 1.4 T, whereas superconducting materials such as YBCO in their bulk form have the extraordinary ability to trap magnetic fields an order of magnitude higher, whilst being very compact. This gives them the potential to increase efficiency and allow significant volume and weight reductions for rotating machines despite the need for cooling. A new design of superconducting magnetic bearing has been developed which uses magnetized bulks as the field source, eliminating permanent magnets. Finite element modelling shows that the bulk – bulk design can achieve much higher force densities than existing permanent magnet – bulk designs, giving it potential to be used as a compact magnetic bearing. A system was created to magnetize bulks using a pulsed magnetic field down to 10 K and then measure levitation force. In proving the concept of the proposed design, the highest levitation forces ever reported between two superconducting bulks were measured, including a levitation force of 500 N between a 1.7 T magnetized YBCO bulk and a coaxial $MgB2$ bulk tube. The biggest factor limiting the use of magnetized bulks in applications is magnetizing them in the first place. Using a pulsed magnetic field is most practical but generates excessive heat dissipation leading to a loss of flux in conventional bulk superconductors, which are 100% superconductor. Although multi-pulse techniques help maximise the trapped field, the poor thermal properties of bulk (RE)BCO are a limiting factor. New composite superconducting structures are reported which can overcome these problems by using high thermal conductivity materials, the motivation for which came from finite element modelling of the critical state coupled with heat transfer. In particular, composite structures created by cutting and stacking 12 mm wide (RE)BCO superconducting tape are shown experimentally to have exceptional field trapping ability due to superior thermal and mechanical properties compared to existing bulks. Up to 2 T was trapped in a stack of commercially available tape produced by SuperPower Inc. in the first reported pulsed magnetization of such a stack. Over 7 T was trapped between two stacks using field cooling at 4.2 K, the highest field yet trapped in such a sample.