  Using data from Gaia DR3, we construct a sample of 14,791 gravitationally
bound wide pairs in which one of the components is an unresolved binary with an
astrometric orbital or acceleration solution. These systems are hierarchical
triples, with inner binary separations of order $1$ au, and outer separations
of $100$-$100,000$ au. Leveraging the fact that the inner binary and outer
tertiary should have nearly identical parallaxes, we use the sample to
calibrate the parallax uncertainties for orbital and acceleration binary
solutions. We find that the parallax uncertainties of orbital solutions are
typically underestimated by a factor of $1.3$ at $G>14$, and by a factor of
$1.7$ at $G = 8$-$14$. The true parallax uncertainties are nevertheless a
factor of $\sim 10$ smaller than those of the single-star astrometric solutions
for the same sources. The parallax uncertainties of acceleration solutions are
underestimated by larger factors of $2$-$3$ but still represent a significant
improvement compared to the sources' single-star solutions. We provide
tabulated uncertainty inflation factors for astrometric binary solutions and
make the catalog of hierarchical triples publicly available.
