Giant permittivity (GP) materials are of interest as possible capacitors for energy storage. Ferroelectric and related homogeneous materials suffer from strongly temperature dependent dielectric properties. Therefore, within the last two decades, the interest has been focused to dielectric studies of various inhomogeneous GP materials, where the essential role was shown to be due to weak but inhomogeneous conductivity. Here we study, within the known models based on effective medium approximation, the broadband dielectric spectra of conducting core – less conducting shell structures, which are expected to be the most advantageous for revealing the GP effects. Examples of core–shell structures, in which the dielectric properties of both components are independent of frequency, are studied analytically and numerically within the generalized brick model. For the simple case of coated-spheres model the dielectric dispersion is of a single Debye-relaxation type and the optimal GP properties are for highly conducting cores and thinnest possible nonconducting and high-permittivity shells. For non-spherical core–shell particles the conditions for macroscopically isotropic composite are briefly discussed.