I searched for the ground state 6.8 and 9.2 GHz hyperfine transitions of rubidium and cesium toward M- and L-dwarfs that show Rb and Cs optical resonance lines. The optical lines can pump the hyperfine transitions, potentially forming masers. These spin-flip transitions of Rb and Cs are the principal transitions used in atomic clocks (the 133Cs hyperfine transition defines the second). If they are detected in stellar atmospheres, these transitions would provide exceptionally precise clocks that can be used as accelerometers, as exoplanet detectors, as probes of the predictions of general relativity, as probes of light propagation effects, and as a means to do fundamental physics with telescopes. Observations of 21 M- and L-dwarfs, however, show no evidence for Rb or Cs maser action, and a previous survey of giant stars made no Rb maser detections.