The need to bridge the THz gap is stimulated by a growing number of important applications including biochemical spectroscopy, plasma turbulence diagnostics and drive sources for tokamaks. Cherenkov sources based on two-dimensional (2D) corrugated surface lattice interaction structures, in which the diameter is several times greater than the radiation wavelength, hold strong promise to bridge the THz gap. In this paper, we demonstrate the ability to drive these sources, typically intended for steady-state operation, into the highly non-linear superradiant regime. We demonstrate, for the first time, the ability to generate superradiant pulses, for which the peak power scales as the number of electrons in the bunch squared, by exploiting slippage of an electron beam through subluminal surface waves close to the metallic 2D corrugation. The surface waves are scattered into low order, forward propagating TM0,N modes which form the emitted 'super pulse'. To drive superradiance, the nanosecond electron bunch must have a fast rising edge with a suitably high (kiloamperes) electron current. Superradiant pulses have been simulated for cases where the relative difference between the group speed of the electromagnetic wave and the drift speed of the electron beam is in the correct range. We show that, for this transient process, the diameter-to-wavelength ratio of the interaction cavities can be scaled from 6 to 9, with a corresponding uplift in peak power from 450 MW to 750 MW, demonstrating the potential for exceptionally powerful THz pulses. The presented results have been obtained for a Cherenkov maser operating in the 83–94 GHz range. However, numerical dispersion analysis, validated by full-wave simulations, shows the potential to radically modify the wave dispersion by varying the 2D lattice geometry for highly controllable, powerful signals at any frequency from 1 GHz to 1 THz. Based on these results, the capability to eventually generate gigawatt-level pulses in the THz range can be projected.