A single-hole probe was designed to measure steady and periodic flows with high fluctuation amplitudes and with minimal flow intrusion. Because of its high aspect ratio, estimations showed that the probe resonates at a frequency two orders of magnitude lower than the fast response sensor cut-off frequencies. The high fluctuation amplitudes cause a non-linear behavior of the probe and available models are neither adequate for a quantitative estimation of the resonating frequencies nor for predicting the system damping. Instead, a non-linear data correction procedure based on individual transfer functions defined for each harmonic contribution is introduced for pneumatic probes that allows to extend their operating range beyond the resonating frequencies and linear dynamics. This data correction procedure was assessed on a miniature single-hole probe of 0.35 mm inner diameter which was designed to measure flow speed and direction. For the reliable use of such a probe in periodic flows, its frequency response was reproduced with a siren disk, which allows exciting the probe up to 10 kHz with peak-to-peak amplitudes ranging between 20%–170% of the absolute mean pressure. The effect of the probe interior design on the phase lag and amplitude distortion in periodic flow measurements was investigated on probes with similar inner diameters and different lengths or similar aspect ratios (L/D) and different total interior volumes. The results suggest that while the tube length consistently sets the resonance frequency, the internal total volume affects the non-linear dynamic response in terms of varying gain functions. A detailed analysis of the introduced calibration methodology shows that the goodness of the reconstructed data compared to the reference data is above 75% for fundamental frequencies up to twice the probe resonance frequency. The results clearly suggest that the introduced procedure is adequate to capture non-linear pneumatic probe dynamics and to reproduce time-resolved data far above probe resonant frequency.