A new theory is developed to evaluate longitudinal and transverse impedances of any size of ceramic break that is sandwiched between metal chambers. The theory has been numerically compared with the codes ABCI and CST STUDIO. Excellent agreements are obtained with both codes, in particular with ABCI. The theory successfully reproduces resonance structures of the impedance due to trapped modes inside the ceramic break, which are enhanced by the difference of the dielectric constants between the ceramic and the surrounding space. Moreover, the theory can evaluate the impedance of the ceramic break with titanium nitride coating. We discuss several characteristics of the impedances, especially the difference between the impedances of the ceramic break covered with and without a conductive wall on its outer surface.