  Here we present speckle observations of 16 low-separation ($s<30$ AU) high
probability candidate binaries from the catalog by Medan et al., where
secondaries typically lack astrometric solutions in Gaia. From these speckle
observations, we find a second component is always detected within the field of
view. To determine if the detection is consistent with a physical companion or
a chance alignment with a background source, we utilize a statistic from
Tokovinin & Kiyaeva that compares the apparent motion of the systems to the
expected orbital motion ($\mu^\prime$). Using simulated binary orbits, we
construct likelihood distributions of $\mu^\prime$ assuming various total
errors on the measurements. With the hypothesis that the system is a true
binary, we show that large measurement errors can result in $\mu^\prime$ values
higher than expected for bound systems. Using simulated chance alignments, we
also create similar likelihoods to test this alternative hypothesis. By
combining likelihoods of both true binaries and chance alignments, we find that
15 of the 16 candidates are physical systems regardless of the level of
measurement error. Our findings also accommodate all 16 as physical systems if
the average, relative measurement error on the binary separations and position
angles is $\sim4.3\%$, which is consistent with our knowledge of the Gaia and
Gemini speckle pipelines. Importantly, beyond assessing the likelihood of a
true binary vs. chance alignment, this quantitative assessment of the true
average measurement error will allow more robust error estimates of mass
determinations from short separation binaries with Gaia and/or Gemini speckle
data.
