Schottky mass spectrometry is a novel method of precision nuclear mass spectrometry based on the measurement of the revolution frequencies of ions in a storage ring. The measurements are performed by non-destructive detection and frequency analysis of the beam noise, the well-established Schottky diagnosis technique. Schottky mass spectrometry was applied for the first time at the Experimental Storage Ring ESR at GSI using electron-cooled, highly charged (mainly bare, H- and He-like) heavy ions at relativistic energies of up to 370 MeV/u. The performance of the method at the ESR is shortly reviewed and an overview of the results from our first mass measurements of radioactive neutron-deficient gold and bismuth fragments is given. Relative accuracies down to 3 x 10^-7 were achieved for the measured masses, corresponding to absolute uncertainties of 50 to 150 keV/c² for these heavy isotopes (135 ≤ A ≤ 209). The typical mass resolving power of about 350000 allows even the resolution of isomeric from ground state masses in some cases. Due to the required cooling time, the method is applicable, so far, to nuclei with half-lives of at least a few seconds.