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Energetic charged particles trapped in planetary radiation belts are hazardous to spacecraft. Planned missions to iron‐rich asteroids with possible strong remanent magnetic fields require an assessment of trapped particles energies. Using laboratory measurements of iron meteorites, we estimate the largest possible asteroid magnetic moment. Although weak compared to moments of planetary dynamos, the small body size may yield strong surface fields. We use hybrid simulations to confirm the formation of a magnetosphere with an extended quasi‐dipolar region. However, the short length scale of the field implies that energetic particle motion would be nonadiabatic, making existing radiation belt theories not applicable. Our idealized particle simulations demonstrate that chaotic motions lead to particle loss at lower energies than those predicted by adiabatic theory, which may explain the energies of transiently trapped particles observed at Mercury, Ganymede, and Earth. However, even the most magnetized asteroids are unlikely to stably trap hazardous particles. Plain Language Summary: Radiation belts are regions in space filled with energetic charged particles trapped by a planetary magnetic field. To date, radiation belts were found around Earth, Jupiter, Saturn, Uranus, and Neptune. Understanding radiation belts is important because they can be hazardous to spacecraft. In addition, their emission, if detected remotely, can reveal a planet's magnetic field. The future exploration of asteroids and exoplanets may lead to the discovery of more magnetized bodies, including the upcoming NASA mission to asteroid (16) Psyche, the largest known metal‐rich planetary object. Existing radiation belt theory was developed for known radiation belts surrounding the large, highly magnetized planets in the solar system. However, the nature of particle trapping should differ for small bodies like asteroids. We examine these differences to provide predictive tools for the existence of belts that can be applied to any kind of magnetosphere. We find a class of bodies that can sustain belt‐like structures but where particle trajectories are chaotic, preventing prolonged stable trapping and associated energization. We show that Mercury and Ganymede's transient trapping is consistent with our predictions. Finally, we show that although asteroids may stably trap low‐energy protons and electrons, even the most strongly magnetized metallic asteroids cannot form belts that pose a risk to typical spacecraft hardware. Key Points: Meteorite paleomagnetism and hybrid modeling imply that asteroids may form magnetospheres and trap charged particlesPlanning of missions to asteroids requires assessing trapped particle energies, but existing models are not valid for such magnetospheresA new nonadiabatic trapping criterion shows that asteroids should not have hazardous particle radiation belts [ABSTRACT FROM AUTHOR]