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We present Mon-735, a detached double-lined eclipsing binary (EB) member of the $\sim$3 Myr old NGC 2264 star forming region, detected by Spitzer. We simultaneously model the Spitzer light curves, follow-up Keck/HIRES radial velocities, and the system's spectral energy distribution to determine self-consistent masses, radii and effective temperatures for both stars. We find that Mon-735 comprises two pre-main sequence M dwarfs with component masses of $M = 0.2918 \pm 0.0099$ and $0.2661 \pm 0.0095$ $\rm{M}_{\odot}$, radii of $R = 0.762 \pm 0.022$ and $0.748 \pm 0.023$ $\rm{R}_{\odot}$, and effective temperatures of $T_{\rm eff} = 3260 \pm 73$ and $3213 \pm 73$ $\rm{K}$. The two stars travel on circular orbits around their common centre of mass in $P = 1.9751388 \pm 0.0000050$ days. We compare our results for Mon-735, along with another EB in NGC 2264 (CoRoT 223992193), to the predictions of five stellar evolution models. These suggest that the lower mass EB system Mon-735 is older than CoRoT 223992193 in the mass-radius diagram (MRD) and, to a lesser extent, in the Hertzsprung-Russell diagram (HRD). The MRD ages of Mon-735 and CoRoT 223992193 are $\sim$7-9 and 4-6 Myr, respectively, with the two components in each EB system possessing consistent ages.