ABSTRACT Understanding the evolution of satellite galaxies of the Milky Way (MW) and M31 requires modelling their orbital histories across cosmic time. Many works that model satellite orbits incorrectly assume or approximate that the host halo gravitational potential is fixed in time and is spherically symmetric or axisymmetric. We rigorously benchmark the accuracy of such models against the FIRE-2 cosmological baryonic simulations of MW/M31-mass haloes. When a typical surviving satellite fell in ($3.4\!-\!9.7\, \rm {Gyr}$ ago), the host halo mass and radius were typically 26–86 per cent of their values today, respectively. Most of this mass growth of the host occurred at small distances, $r\lesssim 50\, \rm {kpc}$, opposite to dark matter only simulations, which experience almost no growth at small radii. We fit a near-exact axisymmetric gravitational potential to each host at z = 0 and backward integrate the orbits of satellites in this static potential, comparing against the true orbit histories in the simulations. Orbital energy and angular momentum are not well conserved throughout an orbital history, varying by 25 per cent from their current values already $1.6\!-\!4.7\, \rm {Gyr}$ ago. Most orbital properties are minimally biased, ≲10 per cent, when averaged across the satellite population as a whole. However, for a single satellite, the uncertainties are large: recent orbital properties, like the most recent pericentre distance, typically are ≈20 per cent uncertain, while earlier events, like the minimum pericentre or the infall time, are ≈40–80 per cent uncertain. Furthermore, these biases and uncertainties are lower limits, given that we use near-exact host mass profiles at z = 0.