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 geometries. The results also show that during the blow-off transient, the total heat release gradually decreases over a duration that agrees well with experiment. The evolution of localized extinction, reactive scalars and scalar dissipation rate is analyzed. It has been observed that a consistent symptom for flames approaching blow-off is the appearance of high-frequency and high-magnitude fluctuations of the conditionally filtered stoichiometric scalar dissipation rate, resulting in an increased fraction of local extinction over the stoichiometric mixture fraction iso-surfaces. It is also shown that the blow-off time changes with the different blow-off conditions.