In principle, band-limited coronagraphic image masks are capable of removing all on-axis starlight providing infinite dynamic range for the direct imaging of exoplanets. In practice, optical aberrations left uncorrected by the adaptive optics system and practical limitations on mask alignment prevent band-limited masks from reaching contrast levels necessary for exoplanet imaging. So-called, “high-order” band-limited masks reduce the coronagraph's sensitivity to low order aberrations, and have been measured to reach contrast levels of $10^{-7}$ at $4\, \lambda/D$ without the aid of a deformable mirror. In this work, we simulate the performance of high-order band-limited coronagraphic image masks in a variety of adaptive optics systems. We compare their performance with that of hard-edge stops, soft-edge Gaussian masks, and traditional (4th-order) band-limited coronagraphs.