We inverted the macroseismic intensity data set (felt reports) of the M 5.4 earthquake of 1990 in SE Sicily and retrieved source parameters that were compatible with those obtained independently by other authors who treated instrumental observations. Our technique uses Voronoi polygons and our kinematic function KF. After this validation, we attempted the inversion of the macroseismic intensity data set of one of the strongest earthquakes that has ever struck the Mediterranean basin (in 1693 in southeast Sicily; 54,000 casualties). It was possible to invert the regional intensity patterns of these two earthquakes because their data sets are sufficiently uncontaminated by local site responses and retain regional traces of source effects. The 1693 source, constrained by our inversion, is a NNE-oriented fault, approximately 60 km long, dipping from 90° to 54° (80° with positive error of 10°, and negative error of 26°) toward ESE, 50% strike-slip and 50% dip-slip, which crosses SE Sicily from the Hyblean Plateau to the coast of the Ionian Sea, south of the city of Catania; the nucleation is 37.08° N 14.93° E. This source best fits the regional distribution of damage observed in the field. At the limit of the negative error of the dip angle, a value of 54° makes our line source, at depth, compatible with the trace of the Scicli active transcurrent fault, which is 12-14 km to the west. The retrieved source is also compatible with the orientation of the maximum horizontal geodynamical compressive stress, confidently measured in the area, as well as with an authoritative tectonic interpretation, independent from this study. The combined use of tessellation and of our KF model is promising for inverting intensity data sets of preinstrumental earthquakes.