Fiber Bragg gratings (FBGs) are well-suited for embedded sensing of interfacial phenomena in materials systems, due to the sensitivity of their spectral response to locally non-uniform strain fields. Over the last 15 years, FBGs have been successfully employed to sense delamination at interfaces, with a clear emphasis on planar events induced by transverse cracks in fiber-reinforced plastic laminates. We have built upon this work by utilizing FBGs to detect circular delamination events at the interface between epoxy films and alumina substrates. Two different delamination processes are examined, based on stress relief induced by indentation of the epoxy film or by cooling to low temperature. We have characterized the spectral response pre- and post-delamination for both simple and chirped FBGs as a function of delamination size. We show that delamination is readily detected by the evolution of a non-uniform strain distribution along the fiber axis that persists after the stressing condition is removed. These residual strain distributions differ substantially between the delamination processes, with indentation and cooling producing predominantly tensile and compressive strain, respectively, that are well-captured by Gaussian profiles. More importantly, we observe a strong correlation between spectrally-derived measurements, such as spectral widths, and delamination size. Our results further highlight the unique capabilities of FBGs as diagnostic tools for sensing delamination in materials systems.