The area-characteristic, maximum possible earthquake magnitude TM is required by the earthquake engineering community, disaster management agencies and the insurance industry. The Gutenberg–Richter law predicts that earthquake magnitudes M follow a truncated exponential distribution. In the geophysical literature, several estimation procedures were proposed, see for instance, Kijko and Singh (Acta Geophys 59(4):674–700, 2011) and the references therein. Estimation of TM is of course an extreme value problem to which the classical methods for endpoint estimation could be applied. We argue that recent methods on truncated tails at high levels (Beirlant et al. Extremes 19(3):429–462, 2016; Electron J Stat 11:2026–2065, 2017) constitute a more appropriate setting for this estimation problem. We present upper confidence bounds to quantify uncertainty of the point estimates. We also compare methods from the extreme value and geophysical literature through simulations. Finally, the different methods are applied to the magnitude data for the earthquakes induced by gas extraction in the Groningen province of the Netherlands.