A pulse-compression technique has been applied to air-coupled testing of solid materials. Capacitance transducers were used to generate wide bandwidth swept-frequency (chirp) signals in air, which were then used to measure and image solid samples in through transmission. The results demonstrate that such signal processing techniques lead to an improvement in the signal to noise ratio and timing accuracy for air-coupled testing. Measurements of thickness and spectroscopic experiments are presented. Images of defects in a wide range of materials, including metals and carbon-fibre composites have also been obtained. This combination of capacitive transducers with pulse-compression techniques is shown to be a powerful tool for non-contact air-coupled ultrasonic measurements.