An approach developed on the basis of a model of a composite with heterogeneous inclusions—the effective-field approximation—is proposed. With the help of this approximation, an expression is obtained for the tensor of effective dielectric characteristics of a heterogeneous medium consisting of inclusions representing a core inside a coating, the outer and inner boundaries of which are ellipsoids. The proposed approach has a large degree of generality and can be used both for multicomponent composites and for polycrystals. It was shown that this approach gives the same result as the generalized singular approximation in the case of the uncoated inclusions.