An electronic device has wireless communications circuitry including an adjustable antenna system coupled to a radio-frequency transceiver. The adjustable antenna system may include one or more adjustable electrical components that are controlled by storage and processing circuitry in the electronic device. The adjustable electrical components may include switches and components that can be adjusted between numerous different states. The adjustable electrical components may be coupled between antenna system components such as transmission line elements, matching network elements, antenna elements and antenna feeds. By adjusting the adjustable electrical components, the storage and processing circuitry can tune the adjustable antenna system to ensure that the adjustable antenna system covers communications bands of interest.