  The realm of strong classical gravity and perhaps even quantum gravity are
waiting to be explored. In this letter we consider the recently detected triple
system composed of two stars and a non-accreting black hole. Using published
observations of this system we conduct the most sensitive test to date for
whether the black hole is actually a wormhole by looking for orbital
perturbations due to an object on the other side of the wormhole. The mass
limit obtained on the perturber is $\sim4$ orders of magnitude better than for
observations of S2 orbiting the supermassive black hole at Sgr A*. We also
consider how observations of a pulsar could test for whether the black hole in
a pulsar-black hole binary is a wormhole. A pulsar in a similar orbit to S2
would be $\sim10$ orders of magnitude more sensitive than observations of S2.
For a nominal pulsar-black hole binary of stellar masses, with orbital size
similar to that of the Hulse-Taylor binary pulsar, one year of observations
could set a mass limit on a perturber that is $\sim6$ orders of magnitude
better than observations of a pulsar around Sgr~A*. A range of limits between
the pulsar-Sgr~A* and Hulse-Taylor cases could be obtained for a possible
population of pulsar-black hole binaries that may exist near the galactic
center.
