The Large Eddy Simulation (LES)/three-dimensional Conditional Moment Closure (CMC) model with detailed chemistry is applied to predict the operating condition and dynamics of complete extinction (blow-off) in swirling non-premixed methane flames. Using model constants previously selected to provide relatively accurate predictions of the degree of local extinction in the piloted jet flames Sandia D−F, the error in the blow-off air velocity predicted by LES/3D-CMC in short, recirculating flames with strong swirl for a range of fuel flow rates is within 25 % of the experimental value, which is considered a new and promising result for combustion LES that has not been applied before for the prediction of the whole blow-off curve in complex geom...