Many efforts have been made to quickly estimate the maximum run-up height of tsunamis associated with large earthquakes. This is a difficult task, because of the time it takes to construct a tsunami model using real time data from the source. It is possible to construct a database of potential seismic sources and their corresponding tsunami a priori.However, such models are generally based on uniform slip distributions and thus oversimplify the knowledge of the earthquake source. Here, we show how to predict tsunami run-up from any seismic source model using an analytic solution, that was specifically designed for subduction zones with a well defined geometry, i.e., Chile, Japan, Nicaragua, Alaska. The main idea of this work is to provide a tool for emergency response, trading off accuracy for speed. The solutions we present for large earthquakes appear promising. Here, run-up models are computed for: The 1992 Mw 7.7 Nicaragua Earthquake, the 2001 Mw 8.4 Perú Earthquake, the 2003Mw 8.3 Hokkaido Earthquake, the 2007 Mw 8.1 Perú Earthquake, the 2010 Mw 8.8 Maule Earthquake, the 2011 Mw 9.0 Tohoku Earthquake and the recent 2014 Mw 8.2 Iquique Earthquake. The maximum run-up estimations are consistent with measurements made inland after each event, with a peak of 9 m for Nicaragua, 8 m for Perú (2001), 32 m for Maule, 41 m for Tohoku, and 4.1 m for Iquique. Considering recent advances made in the analysis of real time GPS data and the ability to rapidly resolve the finiteness of a large earthquake close to existing GPS networks, it will be possible in the near future to perform these calculations within the first minutes after the occurrence of similar events. Thus, such calculations will provide faster run-up information than is available from existing uniform-slip seismic source databases or past events of pre-modeled seismic sources.