The ability to generate a permanent, stable magnetic field unsupported by an electromotive force is fundamental to a variety of engineering applications. Bulk high temperature superconducting (HTS) materials can trap magnetic fields of magnitude over ten times higher than the maximum field produced by conventional magnets, which is limited practically to rather less than 2 T. In this paper, two large c-axis oriented, single-grain YBCO and GdBCO bulk superconductors are magnetized by the pulsed field magnetization (PFM) technique at temperatures of 40 and 65 K and the characteristics of the resulting trapped field profile are investigated with a view of magnetizing such samples as trapped field magnets (TFMs) in situ inside a trapped flux-type superconducting electric machine. A comparison is made between the temperatures at which the pulsed magnetic field is applied and the results have strong implications for the optimum operating temperature for TFMs in trapped flux-type superconducting electric machines. The effects of inhomogeneities, which occur during the growth process of single-grain bulk superconductors, on the trapped field and maximum temperature rise in the sample are modelled numerically using a 3D finite-element model based on the H-formulation and implemented in Comsol Multiphysics 4.3a. The results agree qualitatively with the observed experimental results, in that inhomogeneities act to distort the trapped field profile and reduce the magnitude of the trapped field due to localized heating within the sample and preferential movement and pinning of flux lines around the growth section regions (GSRs) and growth sector boundaries (GSBs), respectively. The modelling framework will allow further investigation of various inhomogeneities that arise during the processing of (RE)BCO bulk superconductors, including inhomogeneous Jc distributions and the presence of current-limiting grain boundaries and cracks, and it can be used to assist optimization of processing and PFM techniques for practical bulk superconductor applications.