  Recent observations by TESS revealed the existence of circumbinary planets in
the systems of TOI-1338 and TIC-172900988. The purpose of this work is to model
the planetary orbits in these two systems and study them under the perspective
of previous theoretical models. Each planet's distance from the barycenter
through time is simulated using n-body integrations and is compared with
outcomes from a semi-analytic, a geometric and a Keplerian-based approach.
Furthermore, we infer the most prominent frequencies of both planets' orbits
induced by the central binaries. We confirm that both systems appear to be
stable. Lastly, we examine the implications of an additional candidate planet
in TOI-1338 system finding that an extra, 48 M$_\oplus$ planet that has been
hinted from observations could be located at 0.8 AU without generating any
radical changes to the orbits of the other members of the system.
