  We derive analytic estimates for the ability with which one can obtain
precise, empirical stellar masses and radii via single-lined eclipsing binaries
(EBs) in the era of {\it Gaia\/} and {\it TESS}. Including stars that host
transiting substellar companions, such single-lined EBs already number in the
hundreds from ground-based transit surveys and will comprise a major component
of the science yield from the upcoming {\it TESS\/} mission. We explore the
requirements for obtaining a given fractional precision on the masses and radii
of single-lined EBs using primarily empirical means: radial velocity and
eclipse measurements along with either: estimates of the primary's (1) surface
gravity from high-resolution spectroscopy; (2) radius inferred from parallax,
effective temperature, and bolometric flux; or (3) surface gravity and density
from asteroseismology. We then compare these requirements to the precision
obtained from invoking stellar models or empirical relations. We show that, for
a fiducial transiting hot Jupiter system, precise, accurate, and essentially
model-independent mass and radius measurements for such single-lined EBs will
be possible in the era of \emph{Gaia}. These will be comparable in precision to
those obtained with double-lined EBs. Moreover, the systems for which these
methods can be applied will vastly outnumber double-lined EBs, thereby
possessing the potential to sample a more complete range of stellar types (such
as M dwarfs); these systems will also, in many cases, be more amenable to
precision etallicity and abundance determinations than are double-lined EBs.
