In the early morning of 1888 March 13, roughly 5 km3 of Ritter Island Volcano fell violently into the sea northeast of New Guinea. This event, the largest lateral collapse of an island volcano to be recorded in historical time, flung devastating tsunami tens of metres high on to adjacent shores. Several hundred kilometres away, observers on New Guinea chronicled 3 min period waves up to 8 m high, that lasted for as long as 3 h. These accounts represent the best available first-hand information on tsunami generated by a major volcano lateral collapse. In this article, we simulate the Ritter Island landslide as constrained by a 1985 sonar survey of its debris field and compare predicted tsunami with historical observations. The best agreement occurs for landslides travelling at 40 m s-1, but velocities up to 80 m s-1 cannot be excluded. The Ritter Island debris dropped little more than 800 m vertically and moved slowly compared with landslides that descend into deeper water. Basal friction block models predict that slides with shorter falls should attain lower peak velocities and that 40+ m s-1 is perfectly compatible with the geometry and runout extent of the Ritter Island landslide. The consensus between theory and observation for the Ritter Island waves increases our confidence in the existence of mega-tsunami produced by oceanic volcano collapses two to three orders of magnitude larger in scale.