We examine the interior electromagnetic energy density of a coated nonabsorbing sphere at a number of scattering resonances. As is the case for an uncoated sphere, the interior energy density becomes large at the a(p)(l) and b(p)(l) resonances. It becomes especially large for p - 1 values of the coating thickness at resonance. These p - 1 enhancements are analogous to the interference maxima that occur in the intensity reflectance of two thin films in contact.