  We investigate the accuracy with which the reconnection electric field $E_M$
can be determined from in-situ plasma data. We study the magnetotail electron
diffusion region observed by NASA's Magnetospheric Multiscale (MMS) on
2017-07-11 at 22:34 UT and focus on the very large errors in $E_M$ that result
from errors in an $LMN$ boundary-normal coordinate system. We determine several
$LMN$ coordinates for this MMS event using several different methods. We use
these $M$ axes to estimate $E_M$. We find some consensus that the reconnection
rate was roughly $E_M$=3.2 mV/m $\pm$ 0.06 mV/m, which corresponds to a
normalized reconnection rate of $0.18\pm0.035$. Minimum variance analysis of
the electron velocity (MVA-$v_e$), MVA of $E$, minimization of Faraday residue,
and an adjusted version of the maximum directional derivative of the magnetic
field (MDD-$B$) technique all produce {reasonably} similar coordinate axes. We
use virtual MMS data from a particle-in-cell simulation of this event to
estimate the errors in the coordinate axes and reconnection rate associated
with MVA-$v_e$ and MDD-$B$. The $L$ and $M$ directions are most reliably
determined by MVA-$v_e$ when the spacecraft observes a clear electron jet
reversal. When the magnetic field data has errors as small as 0.5\% of the
background field strength, the $M$ direction obtained by MDD-$B$ technique may
be off by as much as 35$^\circ$. The normal direction is most accurately
obtained by MDD-$B$. Overall, we find that these techniques were able to
identify $E_M$ from the virtual data within error bars $\geq$20\%.
