Solutions to the main problems that limit the sensitivity of an electron magnetic resonance (EMR) spectrometer on the basis of a whispering gallery mode dielectric resonator (WGMDR) are presented. The electromagnetic losses in the transition regions between the overmoded metallic waveguide, the overmoded dielectric waveguide and the mono-mode dielectric waveguide can be avoided by the free space excitation of the resonator that is proved to be very effective for suitably designed resonators. The EMR measurements on high-dielectric-loss samples can be safely developed employing the novel class of “fractional” WGMDRs, in which the usual traveling wave resonator is modified in a structurally stationary wave resonator. Several peculiarities of a fractional WGMDR, investigated both theoretically and experimentally, evidence the advantages of the application of this class of WGMDRs to EMR spectroscopy.