International audienceProject 8 has developed a novel technique, Cyclotron Radiation Emission Spectroscopy (CRES), for direct neutrino mass measurements. A CRES-based experiment on the beta spectrum of tritium has been carried out in a small-volume apparatus. We provide a detailed account of the experiment, focusing on systematic effects and analysis techniques. In a Bayesian (frequentist) analysis, we measure the tritium endpoint as 18553−19+18 (18548−19+19) eV and set upper limits of 155 (152) eV (90% C.L.) on the neutrino mass. No background events are observed beyond the endpoint in 82 days of running. We also demonstrate an energy resolution of 1.66±0.19 eV in a resolution-optimized magnetic trap configuration by measuring 83mKr 17.8-keV internal-conversion electrons. These measurements establish CRES as a low-background, high-resolution technique with the potential to advance neutrino mass sensitivity