A 'double stacked' configuration of dielectric resonators working in whispering gallery modes is discussed in the light of electron spin resonance high-field experiments. The peculiar advantages of this type of resonator are pointed out. A method for calculating analytically the field distribution in the structure 'stacked' resonator-sample is presented. Applications of the results of this method are discussed: it is shown that the sample characteristics have an active role in determining the field distribution in the resonator and in the sample itself. It is also indicated how the filling factor can be controlled in a simple way up to values exceedingly near unity. (C) 1997 Elsevier Science B.V.