The microwave response of three high-density bulk MgB2 samples has been investigated in the linear and nonlinear regimes. The three samples, characterized by different mean size of grains, have been obtained by reactive infiltration of liquid Mg in powdered B preforms. The linear response has been studied by measuring the microwave surface impedance; the nonlinear response by detecting the power radiated by the sample at the second-harmonic frequency of the driving field. Our results suggest that bulk MgB2 prepared by the liquid Mg infiltration technique is particularly promising for manufacturing resonant cavities operating at microwave frequencies