  We highlight some subtleties that affect naive implementations of quadrupolar
and octupolar gravitational waveforms from numerically-integrated trajectories
of three-body systems. Some of those subtleties arise from the requirement that
the source be contained in its "coordinate near zone" when applying the
standard PN formulae for gravitational-wave emission, and from the need to use
the non-linear Einstein equations to correctly derive the quadrupole emission
formula. We show that some of these subtleties were occasionally overlooked in
the literature, with consequences for published results. We also provide
prescriptions that lead to correct and robust predictions for the waveforms
computed from numerically-integrated orbits.
