  The origin of warm Jupiters (gas giant planets with periods between 10 and
200 days) is an open question in exoplanet formation and evolution. We
investigate a particular migration theory in which a warm Jupiter is coupled to
a perturbing companion planet that excites secular eccentricity oscillations in
the warm Jupiter, leading to periodic close stellar passages that can tidally
shrink and circularize its orbit. If such companions exist in warm Jupiter
systems, they are likely to be massive and close-in, making them potentially
detectable. We generate a set of warm Jupiter-perturber populations capable of
engaging in high-eccentricity tidal migration and calculate the detectability
of the perturbers through a variety of observational metrics. We show that a
small percentage of these perturbers should be detectable in the Kepler light
curves, but most should be detectable with precise radial velocity measurements
over a 3-month baseline and Gaia astrometry. We find these results to be robust
to the assumptions made for the perturber parameter distributions. If a
high-precision radial velocity search for companions to warm Jupiters does not
find evidence of a significant number of massive companions over a 3-month
baseline, it will suggest that perturber-coupled high-eccentricity migration is
not the predominant delivery method for warm Jupiters.
