There isn't a direct analogy, but if we zoom way out and describe cavitation as a nonlinear effect that occurs when the amplitude of a disturbance gets too big (in the case of cavitation to large a magnitude of negative pressure relative to the pressure at rest), there are certainly nonlinear effects that occur when the amplitude of an electromagnetic wave is too large. Principally, dielectric breakdown which includes arcing in air and breakdown of solid insulators as well. Electromagnetic design for high power operation often includes avoiding dielectric breakdown, similar to how fluid designs often need to avoid cavitation.

That's often in high voltage transmission lines and other equipment for the power grid, but most of that design is quasi-static rather than being explicitly in the domain of wave effects. But in high power radio transmitters, the need for good impedance matching at each end of a line going from, for example, a transmitter at the base of the tower to an antenna at the top, is directly linked to the need to avoid standing wave effects that lead to high electric fields and dielectric breakdown. The effect is quantified by the standing wave ratio (SWR), which, when it's high, means that the peak electric field is higher than it needs to be by that factor.