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A microwave nondestructive evaluation (NDE) sensor operating in the X-band (8.2 to 12.4 GHz) for detecting thickness or permittivity changes in one layer of multilayered dielectric structures is presented. In particular, detection of defects in the form of permittivity variations in the core layer of a three-layer structure, such as an aircraft radome, is targeted. Using an efficient analytical model for calculating the resonant frequency of a rectangular patch sensor covered with multilayered dielectric structures, the effects of varying the geometric and electrical parameters of the sensor on its performance are analyzed. According to this analysis and other empirical design equations, a resonant patch sensor was designed for good sensitivity to core permittivity changes, adequate penetration depth and spatial resolution. Experimental results showed that one particular sensor is capable of detecting a relative permittivity change as small as Δε = 0.046, can achieve spatial resolution 5 mm, and can inspect permittivity changes to depth 4.35 mm in the core of a three-layer dielectric structure. Measurements on a fiberglass-honeycomb-fiberglass structure containing injected water showed that 0.25 cc (one honeycomb cell) of water can be detected by this sensor.