Optical coherence elastography (OCE) has recently been used to characterize the natural frequencies of delicate tissues (e.g., the human cornea) with sub-micron tissue oscillation magnitudes. Here, we investigate broadband spectrum sample stimulation using a contact-based piezoelectric transducer (PZT) chirp excitation and compare its performance with a non-contact, air-pulse excitation for OCE measurements on 1.0-7.5% agar phantoms and an porcine cornea under intraocular pressures (IOPs) of 5-40 mmHg. The 3-ms duration air-pulse generated a ∼0-840 Hz excitation spectrum, effectively quantifying the first-order natural frequencies in softer samples (e.g., 1.0%-4.0% agar: 239-782 Hz, 198 Hz/%; porcine cornea: 68-414 Hz, 18 Hz/mmHg, IOP: 5-25 mmHg), but displayed limitations in measuring natural frequencies for stiffer samples (e.g., 4.5%-7.5% agar, porcine cornea: IOP ≥ 30 mmHg) or higher order natural frequency components. In contrast, the chirp excitation produced a much wider spectrum (e.g., 0-5000 Hz), enabling the quantification of both first-order natural frequencies (1.0%-7.5% agar: 253-1429 Hz, 181 Hz/%; porcine cornea: 76-1240 Hz, 32 Hz/mmHg, IOP: 5-40 mmHg) and higher order natural frequencies. A modified Bland-Altman analysis (mean versus relative difference in natural frequency) showed a bias of 20.4%, attributed to the additional mass and frequency introduced by the contact nature of the PZT probe. These findings, especially the advantages and limitations of both excitation methods, can be utilized to validate the potential application of natural frequency OCE, paving the way for the ongoing development of biomechanical characterization methods utilizing sub-micron tissue oscillation features.