The suppression of unnecessary radio-electronic noise and the protection of electronic devices from electromagnetic interference by the use of pliable highly microwave radiation absorbing composite materials based on polymers or rubbers filled with conductive and magnetic fillers have been proposed. Since the working frequency bands of electronic devices and systems are rapidly expanding up to the millimeter wave range, the capabilities of absorbing and shielding composites should be evaluated for increasing operating frequency. The point is that the absorption capacity of conductive and magnetic fillers essentially decreases as the frequency increases. Therefore, this paper is devoted to the absorbing capabilities of composites filled with high-loss dielectric fillers, in which absorption significantly increases as frequency rises, and it is possible to achieve the maximum frequency selective of absorption due to electromagnetic and electromechanical resonances.