Tall rigid blocks are prevalent in ancient historical constructions. Such structures are prone to rocking behaviour under strong ground motion, which is recognisably challenging to predict and mitigate. Our study is motivated by the need to provide innovative non-intrusive solutions to attenuate the rocking response of historical buildings and monuments. In this paper, we examine a novel scheme that employs external resonators buried next to the rocking structure as a means to control its seis- mic response. The strategy capitalizes on the vibration absorbing potential of the structure-soil-resonator interaction. Advanced numerical analyses of discrete mod- els under coherent acceleration pulses with rocking bodies of different slenderness ratios under various ground motion intensities highlight the significant vibration absorbing qualities of the external resonating system. The influence of key system parameters such as the mass, stiffness and damping of the resonator and those of the soil-structure-resonator arrangement are studied. Finally, a case study on the evaluation of the response of rocking structures with external resonators under real pulse-like ground-motion records confirms the important reductions in peak seismic rotational demands obtained with the proposed arrangement.