  Many double white dwarf (WD) mergers likely do not lead to a prompt
thermonuclear explosion. We investigate the prospects for observationally
detecting the surviving remnants of such mergers, focusing on the case of
mergers of double Carbon-Oxygen WDs. For $\sim 10^4$ yr, the merger remnant is
observationally similar to an extreme AGB star evolving to become a massive WD.
Identifying merger remnants is thus easiest in galaxies with high stellar
masses (high WD merger rate) and low star formation rates (low birth rate of
$\sim 6-10 \,{\rm M_{\odot}}$ stars). Photometrically identifying merger
remnants is challenging even in these cases because the merger remnants appear
similar to He stars and post-outburst classical novae. We propose that the most
promising technique for discovering WD merger remnants is through their unusual
surrounding photoionized nebulae. We use CLOUDY photoionization calculations to
investigate their unique spectral features. Merger remnants should produce weak
hydrogen lines and strong carbon and oxygen recombination and fine-structure
lines in the UV, optical and IR. With narrow-band imaging or integral field
spectrographs, we predict that multiple candidates are detectable in the bulge
of M31, the outskirts of M87 and other nearby massive galaxies, and the Milky
Way. Our models roughly reproduce the WISE nebula surrounding the Galactic WD
merger candidate IRAS 00500+6713; we predict detectable [Ne\,VI] and [Mg\,VII]
lines with JWST but that the mid-IR WISE emission is dominated by dust not
fine-structure lines.
