The design and tuning of end magnets of a compact 12MeV race-track microtron (RTM) which is under construction at the Technical University of Catalonia are described. These magnets are systems composed of four dipoles with a Rare-Earth Permanent Magnet (REPM) material used as a source of the magnetic field. The magnetic field level is adjusted by means of tuning plungers in the steel poles. We discuss the end magnets design and results of simulations of the field distributions and describe the REPM blocks magnetization and magnetic field measurements applied in this work. Also, the techniques used for the field distribution tuning procedure are explained in detail. Finally, we discuss results of simulations of particle trajectories in the measured magnetic field of the assembled and tuned end magnets and show that they can provide a passage of the synchronous particle through all orbits of the RTM and therefore the correct operation of the machine.