Adiabatic half-passage (AHP) pulses show great promise for significantly enhancing the signal-to-noise ratio of the surface nuclear magnetic resonance (NMR) free-induction decay measurement. Performing an AHP requires that the frequency sweep terminates when the transmit frequency is equal to the Larmor frequency, a condition that demands accurate knowledge of the true Larmor frequency. If the frequency sweep is terminated at an incorrect frequency, i.e., with an unknown offset between the transmit and Larmor frequency at the end of the pulse, the net excitation is affected and it can differ from that predicted by modeling that assumes a 0 Hz offset at the end of the sweep. Surface NMR surveys using a traditional single-frequency pulse have previously been shown to display degraded performance in the presence of an uncertain Larmor frequency estimate; the AHP pulse is also likely susceptible to such degraded performance. To ensure that reliable results can be produced by AHP pulses in the presence of an uncertain Larmor frequency estimate, we have developed an approach that adapts the frequency-cycling scheme for use with AHP pulses. We hypothesize that data collected using two similar AHP pulses, each with the exact same frequency sweep but where one sweeps toward the Larmor frequency from higher frequencies and the other from lower frequencies, can be stacked in such a manner that the impact of an unknown frequency offset is significantly reduced. We present synthetic and field results to demonstrate that frequency-cycling AHP pulse surface NMR data can ensure reliable performance even in the presence of an uncertain Larmor frequency estimate.