We have used a mono‐ion oscillator to demonstrate the usefulness of a spectroscopic technique for achieving high‐resolution frequency measurements in the presence of anharmonicity. The technique uses a noise‐free parametric process to amplify a weakly pre‐excited oscillator that allows one to reduce anharmonic frequency shift and at the same time to detect the resonance signal with large amplitude. In our initial experiments using the parametric process, 100 times narrower spectral lines have been obtained. The technique is potentially useful in such high‐precision experiments as the electrong‐2 measurement and the ion mass spectroscopy in Penning traps. The possibility of using the parametric process to detect then=0→n=1 transition of the cyclotron motion in geonium is also discussed.