  Early-type main-sequence pulsating stars such as \ds{} variables are one of
the least explored class of targets in the search for exoplanets. Pulsation
timing (PT) is an alternative technique to the most effective search methods.
It exploits the light-travel-time effect (LTTE) to infer the presence of
additional massive bodies around a pulsating star by measuring a periodic phase
modulation of its signal. PT has been extremely successful in discovering and
characterizing stellar binaries when it was applied to high-precision light
curves over long temporal baselines, such as those delivered by the Kepler
mission. In favorable conditions, the sensitivity of PT can reach the
planetary-mass regime; one such candidate has already been claimed. The advent
of TESS, with its nearly full-sky coverage and the availability of full-frame
images, opens a great opportunity to expand this field of research. In this
work, we present a pilot study aimed to understand the potential of PT as
applied to TESS data, which are considerably different from Kepler data in
terms of photometric noise, sampling cadence, and temporal baseline. We focused
on the most favorable class of \ds{}, that is, those showing strong pulsations
and very simple frequency spectra. After the development of a customized
pipeline, we were able to detect candidate companions for two targets in the
(sub-)stellar mass regime: Chang~134 ($43\pm 5$~$M_\mathrm{jup}$, $P\simeq
82$~d) and V393 Car ($\gtrsim 100$~$M_\mathrm{jup}$, $P\gtrsim 700$~d). Our
results also highlight the limiting factors of this technique and the
importance of an accurate absolute time calibration for future missions such as
PLATO.
