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We present an apparatus for detection of cyclotron radiation yielding a frequency-based β  kinetic energy determination in the 5 keV to 2.1 MeV range, characteristic of nuclear β decays. The cyclotron frequency of the radiating β particles in a magnetic field is used to determine the β energy precisely. Our work establishes the foundation to apply the cyclotron radiation emission spectroscopy (CRES) technique, developed by the Project 8 Collaboration, far beyond the 18-keV tritium endpoint region. We report initial measurements of β−’s from 6He and βþ’s from 19Ne decays to demonstrate the broadband response of our detection system and assess potential systematic uncertainties for β spectroscopy over the full (MeV) energy range. To our knowledge, this is the first direct observation of cyclotron radiation from individual highly relativistic β’s in a waveguide. This work establishes the application of CRES to a variety of nuclei, opening its reach to searches for new physics beyond the TeV scale via precision β-decay measurements.