In many resonant structures the damping of parasitic or higher order modes is indispensable to guarantee a correct and stable performance. This is particularly true in the microwave region in case of cavities or other resonant systems operating in accelerating structures, where the mitigation of spurious resonance effects is mandatory to achieve high quality particle beams. We present the results on the mode suppression in a real pillbox cavity by inserting a properly designed pyramidal metamaterial that acts as light, small volume damper for specific resonances in the range 3-4 GHz, only slightly perturbing other intrinsic modes. Measurements of the cavity response without and with the metamaterial absorber are presented and compared with full wave simulations. Field distribution for the pillbox intrinsic modes under scrutiny is also presented, showing that damping induced by the metamaterial critically depends on its relative position inside the cavity.