A non-linear shunt circuit is coupled in a shunt-type configuration (e.g., parallel to an RF switch shunt branch) between a main signal line and ground in an RF circuit, and includes a harmonic cancellation element (HCE) (e.g., back-to-back diodes or diode-connected FETs) configured to cancel third harmonics generated on the main signal line by operation of an RF switch. The RF switch includes a series branch made up of multiple FETs coupled in series in the main signal line between a transmitter/receiver circuit and an antenna. The HCE is coupled to the main signal line either by way of a mid-point node or an input/output terminal of the RF switch's series branch. The non-linear shunt circuit also includes optional protection circuits that provide frequency-independent impedance through the HCE. Various techniques (e.g., active biasing) are optionally utilized to increase effectiveness to a wider range of the switch input power levels.