Knowledge of the absolute material nonlinearity parameter, β, of a specimen allows for quantitative evaluation of its current microstructural state, making it a powerful tool in the NDE toolbox. However, the various methods used in the past to measure β each suffer from significant limitations. Piezoelectric contact transducers, while easy to use in many ways, are hindered by the unreliability of the interfacial contact between transducer and specimen surface, which offsets their high sensitivity to nonlinear signals. Laser interferometry provides non-contact detection, but requires carefully prepared specimens or expensive and complicated optics to maximize sensitivity to the nonlinear components of a received waveform, and additionally is expensive and relatively difficult to use in the field. Air-coupled piezoelectric transducers offer the strengths of both of these technologies and the weaknesses of neither, but are notoriously difficult to calibrate for use in nonlinear measurements. This work proposes a hybrid modeling and experimental approach to air-coupled transducer calibration and the use of this calibration in a model-based optimization to determine the β parameter of the material under investigation. This approach is applied to aluminum and fused silica, which are both well-documented materials and provide a strong reference for comparison of experimental and modeling results.