We have applied the Werner-Cary method [J. Comp. Phys. 227, 5200-5214 (2008)] for extracting modes and mode frequencies from time-domain simulations of crab cavities, as are needed for the ILC and the beam delivery system of the LHC. This method for frequency extraction relies on a small number of simulations, and post-processing using the SVD algorithm with Tikhonov regularization. The time-domain simulations were carried out using the VORPAL computational framework, which is based on the eminently scalable finite-difference time-domain algorithm. A validation study was performed on an aluminum model of the 3.9 GHz RF separators built originally at Fermi National Accelerator Laboratory in the US. Comparisons with measurements of the A15 cavity show that this method can provide accuracy to within 0.01% of experimental results after accounting for manufacturing imperfections. To capture the near degeneracies two simulations, requiring in total a few hours on 600 processors were employed. This method has applications across many areas including obtaining MHD spectra from time-domain simulations
