  It has been established that Gamma-Ray Bursts (GRB) can produce Very High
Energy radiation (E > 100 GeV), opening a new window on the investigation of
particle acceleration and radiation properties in the most energetic domain. We
expect that next-generation instruments, such as the Cherenkov Telescope Array
(CTA), will mark a huge improvement in their observation. However, constraints
on the target visibility and the limited duty cycle of Imaging Atmospheric
Cherenkov Telescopes (IACT) reduce their ability to react promptly to transient
events and to characterise their general properties. Here we show that an
instrument based on the Extensive Air Shower (EAS) array concept, proposed by
the Southern Wide Field-of-view Gamma-ray Observatory (SWGO) Collaboration, has
promising possibilities to detect and track VHE emission from GRBs.
Observations made by the Fermi Large Area Telescope (Fermi-LAT) identified some
events with a distinct spectral component, extending above $1\,$GeV or even
$10\,$GeV, which can represent a substantial fraction of the emitted energy and
also arise in early stages of the process. Using models based on these
properties, we estimate the possibilities that a wide field of view and large
effective area ground-based monitoring facility has to probe VHE emission from
GRBs. We show that the ability to monitor VHE transients with a nearly
continuous scanning of the sky grants an opportunity to access simultaneous
electromagnetic counterparts to Multi-Messenger triggers up to cosmological
scales, in a way that is not available to IACTs.
