To communicate, spacecraft and satellites rely on microwave devices, which at present are based on relatively inefficient thermionic electron sources that require heating and cannot be switched on instantaneously. Here we describe a microwave diode that uses a cold-cathode electron source consisting of carbon nanotubes and that operates at high frequency and at high current densities. Because it weighs little, responds instantaneously and has no need of heating, this miniaturized electron source should prove valuable for microwave devices used in telecommunications.