  We present numerical studies of two photonic crystal membrane microcavities,
a short line-defect cavity with relatively low quality ($Q$) factor and a
longer cavity with high $Q$. We use five state-of-the-art numerical simulation
techniques to compute the cavity $Q$ factor and the resonance wavelength
$\lambda$ for the fundamental cavity mode in both structures. For each method,
the relevant computational parameters are systematically varied to estimate the
computational uncertainty. We show that some methods are more suitable than
others for treating these challenging geometries.
