An ultracapacitor or hybrid capacitor includes an electrically non-conductive rigid or semi-rigid porous honeycomb structure (12) having cells extending along a common direction and having an average density per unit area within in a plane perpendicular to the common direction exceeding 15.5 per square centimeter, desirably formed of a material that is stable at temperatures of 300° or more, such that high temperatures processing can be used to help ensure high purity of the final product. The material may desirably be an oxide or non-oxide ceramic, such as cordierite, silicon nitride, alumina, aluminum titanate, zircon, glass, or glass-ceramic.