"I assume that's the full version of UV Mapper, not the free one?"

Yes, only UVMapper Pro can do that.

"The two faces should be touching each other at some points, but I don't see any artifacts."

To answer that, you'd probably need to be the developers of Firefly; and if you are, how come you haven't fixed it yet? :) You see my point, I think.

In general it seems all right for surfaces to be in close proximity to each other as long as it isn't extensive. We know they can intersect without harm, after all. Looking at the blocky nature of the coincident facet artefacts might lead one to believe that the facets had to be coincident over a certain minimum area before anything bad occurred; and further thought suggests that changing some render settings or other might cause this minimum to vary. This is pure hypothesis at the moment.

What I'd really like is proper WYSIWYG preview of single-sided mesh, and we aren't likely to get that here. Many's the time I've set up my perfect camera angle, only to find that there's a single-sided wall that I'd overlooked and my render shows only the backside of said wall. At least such a viewpoint renders quickly. :)

LOL I still do that all the time. Only now I don't usually spend hours and hours trying to work out what's gone wrong.... Usually.... Last time I got caught I spent ages trying to work out what these odd semi-transparent grey splotches were - I must've nudged the carefully positioned (orbiting) camera, pushing it's Y value negative and ending up with  shadows from a shadowcatcher-only groundplane in my render.

Maybe it's not as simple as there being a "minimum separation distance" to avoid these artifacts? Maybe as you suggest it's a combination of render settings, other settings, and how extensive the area of proximity is. I was surprised that the intersecting wiggly waves seemed to show artefacts, whereas the gently tangentially caressing wiggly waves (see, I'm part poet at heart!) didn't seem to show any...

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The 3Dcheapskate (also available in DAZ and HiveWire3D flavours) occasionally posts sensible stuff. Usually by accident.
And it usually uses Poser 11, with units set to inches. Except when it's using Poser 6 or PP2014, or when its units are set to PNU.