We experimentally and numerically investigate a diagnostic method for detecting hidden delamination in composite panels, using highly nonlinear solitary waves. Solitary waves are a type of nonlinear waves with strong energy intensity and non-distortive nature, which can be controllably generated in one-dimensional granular crystals. In this study, we use granular crystals as a combined sensor and actuator to detect hidden delamination in carbon fiber reinforced polymer (CFRP) composite panels. Specifically, we locally excite a CFRP composite specimen using the granular crystal as an actuator and measure the reflected waves that carry the specimen's diagnostic information using the same device as a sensor. We first investigate the effect of the panel's boundary conditions on the response of the reflected solitary waves. We then investigate the interactions of a solitary wave with delamination hidden in the CFRP composite specimen. Lastly, we define a damage index based on the solitary waves' responses to identify the location of the hidden delamination in the CFRP composite panel. The solitary wave-based diagnostic method can provide unique merits, such as portable and fast sensing of composites' hidden damage, thereby with the potential of being used for hot spot monitoring of composite-based structures.