  We consider the frequency-domain LO and NLO post-Minkowskian (PM) waveforms
obtained from the tree-level and one-loop amplitudes describing the scattering
of two massive scalar objects and the emission of one graviton. We explicitly
calculate their post-Newtonian (PN) limit obtaining an expansion up to the
third subleading PN order in all ingredients: the tree-level amplitude, the odd
and even parts of the real one-loop kernel, and the Compton or "rescattering"
cuts, thus reaching 3PN precision for the latter. We provide explicit
expressions for the multipole decomposition of these results in the
center-of-mass frame and compare them with the results obtained from the
classical Multipolar post-Minkowskian (MPM) method. We find perfect agreement
between the two, once the BMS supertranslation frame is properly adjusted and
the infrared divergences due to rescattering are suitably subtracted in
dimensional regularization. This shows that the approach proposed in
arXiv:2312.07452 can be applied beyond the soft-regime ensuring the agreement
between amplitude-based and MPM results for generic frequencies.
