A full orbit code is used to compute collisionless losses of fusion α particles from three proposed burning plasma tokamaks: the International Tokamak Experimental Reactor (ITER); a spherical tokamak power plant (STPP) [T. C. Hender, A. Bond, J. Edwards, P. J. Karditsas, K. G. McClements, J. Mustoe, D. V. Sherwood, G. M. Voss, and H. R. Wilson, Fusion Eng. Des. 48, 255 (2000)]; and a spherical tokamak components test facility (CTF) [H. R. Wilson, G. M. Voss, R. J. Akers, L. Appel, A. Dnestrovskij, O. Keating, T. C. Hender, M. J. Hole, G. Huysmans, A. Kirk, P. J. Knight, M. Loughlin, K. G. McClements, M. R. O’Brien, and D. Yu. Sychugov, Proceedings of the 20th IAEA Fusion Energy Conference, Invited Paper FT∕3-1Ra]. It has been suggested that α particle transport could be enhanced due to cyclotron resonance with the toroidal magnetic field ripple. However, calculations for inductive operation in ITER yield a loss rate that appears to be broadly consistent with the predictions of guiding center theory, falling monotonically as the number of toroidal field coils N is increased (and hence the ripple amplitude is decreased). For STPP and CTF the loss rate does not decrease monotonically with N, but collisionless losses are generally low in absolute terms. As in the case of ITER, there is no evidence that finite Larmor radius effects would seriously degrade fusion α-particle confinement.