  Combining visual and spectroscopic orbits of binary stars leads to a
determination of the full 3D orbit, individual masses, and distance to the
system. We present a full analysis of the evolved binary system $\delta$
Delphini using astrometric data from the MIRC and PAVO instruments on the CHARA
long-baseline interferometer, 97 new spectra from the Fairborn Observatory, and
87 unpublished spectra from Lick Observatory. We determine the full set of
orbital elements for $\delta$ Del, along with masses of $1.78 \pm 0.07$
$M_{\odot}$ and $1.62 \pm 0.07$ $M_{\odot}$ for each component, and a distance
of $63.61 \pm 0.89$ pc. These results are important in two contexts: for
testing stellar evolution models and defining the detection capabilities for
future planet searches. We find that the evolutionary state of this system is
puzzling, as our measured flux ratios, radii, and masses imply a $\sim$ 200 Myr
age difference between the components using standard stellar evolution models.
Possible explanations for this age discrepancy include mass transfer scenarios
with a now ejected tertiary companion. For individual measurements taken over a
span of 2 years we achieve $<10$ $\mu$-arcsecond precision on differential
position with 10-minute observations. The high precision of our astrometric
orbit suggests that exoplanet detection capabilities are within reach of MIRC
at CHARA. We compute exoplanet detection limits around $\delta$ Del, and
conclude that if this precision is extended to wider systems we should be able
to detect most exoplanets $>2$ M$_{J}$ on orbits $>0.75$ AU around individual
components of hot binary stars via differential astrometry.
