Accurate frequency estimation is crucial for Structural Health Monitoring (SHM), as small changes in the dynamic characteristics of a structure can signal damage occurrence. This paper presents a frequency estimation technique based on up- and down-chirp excitation of the structure over a defined, narrow frequency range. During excitation with variable frequency, the structural response is captured. The natural frequency is found when the structure has the same frequency response for increasing and decreasing excitation frequencies. The response data is processed using an advanced frequency estimation algorithm to extract natural frequencies with improved accuracy. Experimental validation is conducted on a laboratory-scale beam structure excited by contactless sound pressure and equipped with an accelerometer. The results demonstrate the superior performance of the chirp-based technique compared to conventional methods, particularly in estimation accuracy and repeatability. We succeeded in finding frequencies with errors less than 0.1 Hz. The technique is especially well-suited for applications requiring early damage detection and can be applied to non-metallic materials.