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Numerical simulations have been used in studies of the temporal and spectral features of supercontinuum generation in photonic crystal and tapered optical fibers. In particular, an ensemble average over multiple simulations performed with random quantum noise on the input pulse allows the coherence of the supercontinuum to be quantified in terms of the dependence of the degree of first-order coherence on the wavelength. The coherence is shown to depend strongly on the input pulse’s duration and wavelength, and optimal conditions for the generation of coherent supercontinua are discussed.