Trapped field measurements were performed on bulk, polycrystalline MgB2 samples from different sources with the emphasis to develop applications like superconducting permanent magnets ('supermagnets') and electric motors. We describe the basic principles and requirements of trapped field measurements and the inductor principle for the design of new effictive superconducting motors. Furthermore, a magnetic and microstructural characterization of the samples is presented. The trapped field measurements were conducted using a cryocooling system to cool the bulk samples to the desired temperatures, and a low-loss cryostat equipped with a room-temperature bore and a maximum field of ±5 T was employed to provide the external magnetic field. The measurements were performed with samples of 20 and 30 mm of diameter. We discuss the results and the problems arising from flux jumping.