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 NASAs 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 $0.18pm0.035$. 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%.
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