The existence of crossover resonances makes saturated-absorption (SA) spectra very complicated when external magnetic field B is applied. It is demonstrated for the first time, to the best of our knowledge, that the use of micrometric-thin cells (MTCs, L≈40 μm) allows application of SA for quantitative studies of frequency splitting and shifts of the Rb atomic transitions in a wide range of external magnetic fields, from 0.2 up to 6 kG (20-600 mT). We compare the SA spectra obtained with the MTC with those obtained with other techniques and present applications for optical magnetometry with micrometer spatial resolution and a broadly tunable optical frequency lock.