The disclosure provides for electrochemical supercapacitors with high energy densities, based on paired groups of carbon nanotube mounted to conductive substrates. In one variation, the electrochemical supercapacitors are double layer capacitors, or electrochemical double layer capacitors, containing opposing groups of carbon nanotubes on opposing substrates. In another variation, the capacitor is an interdigitated capacitor of alternating electrode containing carbon nanotubes, mounted on a common substrate. Processes and devices are also described.