Research data supporting [Portable, desktop high-field magnet systems using bulk, single-grain RE-Ba-Cu-O high-temperature superconductors]. The Microsoft Excel file contains all data plotted in figures 1 to 8 except figure 2 in the main manuscript. Figure 2 is the schematic diagram of the experimental rigs. For all pulsed field magnetization data, the sample was first cooled down from the normal state to the superconducting state then a single pulsed field or a sequence of two pulsed fields (two-step multi-pulse) were applied to it. The values of trapped field shown in the data file are the values recorded at 15 seconds after applying each pulsed field. After reaching the set temperature the wait time before applying a magnetizing pulse was from was from ~5 min (at 77 K) to ~15 min (at 55 K) to allow sufficient time for the sample and the sample holder to reach the thermal equilibrium. Unless stated otherwise, the applied field and the trapped field were the peak value of the magnetizing pulse and the trapped field at the centre of the top surface of each sample, respectively. For the field cooling data, the sample was cooled from room temperature to 77 K, in an applied field of 1.5 T from a copper electromagnet, using a liquid nitrogen bath. The applied field was then removed and the trapped field profiles at 1.5 mm above the top surfaces of the sample were measured. A hand-held gaussmeter was also used to find the maximum trapped field on the surface of each sample. See the main manuscript for more details.