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Abstract Models of near‐field tsunamis and an extreme hurricane provide further evidence for a great precolonial earthquake along the Puerto Rico Trench. The models are benchmarked to brain‐coral boulders and cobbles on Anegada, 125 km south of the trench. The models are screened by their success in flooding the mapped sites of these erratics, which were emplaced some six centuries ago. Among 25 tsunami scenarios, 19 have megathrust sources and the rest posit normal faulting on the outer rise. The modeled storm, the most extreme of 15 hurricanes of category 5, produces tsunami‐like bores from surf beat. In the tsunami scenarios, simulated flow depth is 1 m or more at all the clast sites, and 2 m or more at nearly all, given either a megathrust rupture 255 km long with 7.5 m of dip slip and M8.45, or an outer‐rise rupture 130 km long with 11.4 m of dip slip and M8.17. By contrast, many coral clasts lie beyond the reach of simulated flooding from the extreme hurricane. The tsunami screening may underestimate earthquake size by neglecting trees and shrubs that likely impeded both the simulated flows and the observed clasts; and it may overestimate earthquake size by leaving coastal sand barriers intact. The screening results broadly agree with those from previously published tsunami simulations. In either successful scenario, the average recurrence interval spans thousands of years, and flooding on the nearest Caribbean shores begins within a half‐hour.