  The Lambda-doublet transitions in CH at 3.3 and 0.7 GHz are unusually
sensitive to variations in the fine-structure constant and the
electron-to-proton mass ratio. We describe methods used to measure the
frequencies of these transitions with Hz-level accuracy. We produce a pulsed
supersonic beam of cold CH by photodissociation of CHBr3, and we measure the
microwave transition frequencies as the molecules propagate through a
parallel-plate transmission line resonator. We use the molecules to map out the
amplitude and phase of the standing wave field inside the transmission line. We
investigate velocity-dependent frequency shifts, showing that they can be
strongly suppressed through careful timing of the microwave pulses. We measure
the Zeeman and Stark effects of the microwave transitions, and reduce
systematic shifts due to magnetic and electric fields to below 1 Hz. We also
investigate other sources of systematic uncertainty in the experiment.
