Elastomer composites are prepared by infiltrating polydimethylsiloxane (PDMS) into a porous ceramic structure of nanoparticles. This method differs from the conventional approach, where particles are dispersed into the polymer matrix, since here, the polymer is incorporated into a pre-sintered structure of nanoparticles by infiltration under vacuum. Several oxides (CoFe₂O₄, ZnO, BaTiO₃, BiFeO₃, and BiFeO₃ doped with yttrium), commonly used for dielectric and piezoelectric devices, were infiltrated by PDMS. The porous 3D structure of nanoparticles is obtained by using cellulose as a scaffold and binder, which is eliminated during the process. Thus, the so-called (3,3) composites are obtained, where the particles are in direct contact (although immersed in the polymer), at relatively low loading. The dielectric behaviour of the infiltrated and conventional composites is determined by impedance spectroscopy, dielectric polarization analysis, determinations of electric breakdown-field (E_BD), and static dielectric constant (ε_s). The percentage increase of ε_s from conventional to infiltrated composites is remarkable, reaching for BiFeO₃-Y, an increase of ε_s and ε′(ω) larger than 600 %, while E_BD decreases by a factor of 3.