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We present high-quality ULTRACAM photometry of the eclipsing detached double white dwarf binary NLTT 11748. This system consists of a carbon/oxygen white dwarf and an extremely low mass (<0.2 M☼) helium-core white dwarf in a 5.6 hr orbit. To date, such extremely low-mass white dwarfs, which can have thin, stably burning outer layers, have been modeled via poorly constrained atmosphere and cooling calculations where uncertainties in the detailed structure can strongly influence the eventual fates of these systems when mass transfer begins. With precise (individual precision ≈1%), high-cadence (≈2 s), multicolor photometry of multiple primary and secondary eclipses spanning >1.5 yr, we constrain the masses and radii of both objects in the NLTT 11748 system to a statistical uncertainty of a few percent. However, we find that overall uncertainty in the thickness of the envelope of the secondary carbon/oxygen white dwarf leads to a larger (≈13%) systematic uncertainty in the primary He WD's mass. Over the full range of possible envelope thicknesses, we find that our primary mass (0.136-0.162 M☼) and surface gravity (log (g) = 6.32-6.38; radii are 0.0423-0.0433 R☼) constraints do not agree with previous spectroscopic determinations. We use precise eclipse timing to detect the Rømer delay at 7σ significance, providing an additional weak constraint on the masses and limiting the eccentricity to ecos ω = (– 4 ± 5) × 10–5. Finally, we use multicolor data to constrain the secondary's effective temperature (7600 ± 120 K) and cooling age (1.6-1.7 Gyr). [ABSTRACT FROM AUTHOR]