  Theoretical models of stars constitute a fundamental bedrock upon which much
of astrophysics is built, but large swaths of model parameter space remain
uncalibrated by observations. The best calibrators are eclipsing binaries in
clusters, allowing measurement of masses, radii, luminosities, and
temperatures, for stars of known metallicity and age. We present the discovery
and detailed characterization of PTFEB132.707+19.810, a P=6.0 day eclipsing
binary in the Praesepe cluster ($\tau$~600--800 Myr; [Fe/H]=0.14$\pm$0.04). The
system contains two late-type stars (SpT$_P$=M3.5$\pm$0.2;
SpT$_S$=M4.3$\pm$0.7) with precise masses ($M_p=0.3953\pm0.0020$~$M_{\odot}$;
$M_s=0.2098\pm0.0014$~$M_{\odot}$) and radii ($R_p=0.363\pm0.008$~$R_{\odot}$;
$R_s=0.272\pm0.012$~$R_{\odot}$). Neither star meets the predictions of stellar
evolutionary models. The primary has the expected radius, but is cooler and
less luminous, while the secondary has the expected luminosity, but is cooler
and substantially larger (by 20%). The system is not tidally locked or
circularized. Exploiting a fortuitous 4:5 commensurability between $P_{orb}$
and $P_{rot,prim}$, we demonstrate that fitting errors from the unknown spot
configuration only change the inferred radii by <1--2%. We also analyze subsets
of data to test the robustness of radius measurements; the radius sum is more
robust to systematic errors and preferable for model comparisons. We also test
plausible changes in limb darkening, and find corresponding uncertainties of
~1%. Finally, we validate our pipeline using extant data for GU Boo, finding
that our independent results match previous radii to within the mutual
uncertainties (2--3%). We therefore suggest that the substantial discrepancies
are astrophysical; since they are larger than for old field stars, they may be
tied to the intermediate age of PTFEB132.707+19.810.
