An electronic device has wireless communications circuitry that includes transmitters and receivers. Antenna structures may be coupled to the transmitters and receivers to support radio-frequency signal transmission and radio-frequency signal reception operations. Switching circuitry such as first and second radio-frequency switches may be used to support multiple communications bands of interest. A low band set of transmitters may be associated with the first switch and a high band set of transmitters may be associated with the second switch. The switches can be configured in real time to switch a desired communications band into use. As transmitted signals at frequency f pass through the switches, harmonics at 2f, 3f, and other integral multiples of the transmitted signals may be produced. A diplexer may be interposed between the switching circuitry and the antenna structures that prevents the harmonics from reaching the antenna structures.