Local bathymetry and onshore features can have a substantial effect on the spatial variability of impact from an incoming tsunami. In a warning context, being able to provide localised tsunami forecasts at strategic locations would therefore mitigate the damage posed. Despite the recent advancements in computing powers and the development of highly efficient tsunami codes, capturing this local variability can oftentimes be unfeasible in a warning setting. Traditional high resolution simulations which can capture these localised effects are often too costly to run ‘on-the-fly’. Alternative approaches which capture the localised response to an incoming tsunami, which are based upon utilising the maximum wave heights from a computationally cheap regional forecast, are developed here. These alternative approaches are envisaged to aid in a warning centre’s ability at providing extremely rapid localised forecasts. The approaches focus upon two different methods: transfer functions and machine learning techniques. The transfer functions are based upon recent extensions to the established Green’s Law. The extended versions introduce site specific amplification parameters, with the aim of capturing the neglected localised effects. An automative approach which optimises for these site specific parameters is outlined and the performance of these transfer functions is explored. A machine learning model is also trained and utilised to predict the localised tsunami hazard. Its performance is compared to the extended Green’s Law approach for several sites along the French coast. These developed methods showcase promising techniques that a tsunami warning centre could utilise to provide high resolution warnings.