A method for nondestructive inspection of ceramic structures present as either a ceramic matrix composite structure or a ceramic based coating. Such non-metallic structures are used to provide thermal protection or weight reduction or both to aircraft and their components. The nonmetallic structure is scanned with an electromagnetic pulse in the range of 200 GHz to 4 THz. The electromagnetic pulse includes a plurality of frequencies within the Terahertz range and is not restricted to a single designated frequency. The frequency range is sensitive to changes in impedances and refractive index within the structure. After the electromagnetic pulse passes through the nonmetallic structure, it may be evaluated for changes in impedance in the nonmetallic structure at different locations, and, when present, whether the changes in impedance impact the ability of the structure to perform the function for which it was designed.