Inexpensive radio-frequency devices that can meet the ultrahigh-frequency needs of fifth- and sixth-generation wireless telecommunication networks are required. However, combining high performance with cost-effective scalable manufacturing has proved challenging. Here, we report the fabrication of solution-processed zinc oxide Schottky diodes that can operate in microwave and millimetre-wave frequency bands. The fully coplanar diodes are prepared using wafer-scale adhesion lithography to pattern two asymmetric metal electrodes separated by a gap of around 15 nm, and are completed with the deposition of a zinc oxide or aluminium-doped ZnO layer from solution. The Schottky diodes exhibit a maximum intrinsic cutoff frequency in excess of 100 GHz, and when integrated with other passive components yield radio-frequency energy-harvesting circuits that are capable of delivering output voltages of 600 mV and 260 mV at 2.45 GHz and 10 GHz, respectively. Nanoscale electrodes fabricated using adhesion lithography can be combined with solution-processed metal oxide semiconductors to create Schottky diodes with performance suitable for 5G communications and beyond.