Well, I tried printing a ~ 3600 x 2700 px file at approx 21.5" x 14.25". I upres-ed the file to exactly twice the linear dimension (e.g. 7200 px wide), then cropped to 21.5 x 14.25 at 300 ppi, followed by sharpening, etc. The result was disappointing, and did not have the detail and sharpness I want.
3600 pixels at 21.5 inch output, equals 167 PPI. That will not look very sharp at close viewing distance, but there is something that can be done to improve the situation, although it also depends a bit on the specific image content. Up-sampling by itself will not give you much, although it does allow to get closer to the native printer resolution. That will allow to use a better upsampling algorithm than the printer driver will use, AND you can apply output sharpening at that native printer resolution.
You can also use a dedicated up-sampling program like Benvista's Photozoom Pro. That will
actually add resolution to edge detail, as outlined in this thread
Plan B is to print at 18 x 11.5 to go in an 18 x 24" mat. I am going to print the original file without upsampling (will be about 200ppi, which is low!) as well as the upsampled file cropped to this dimension (at 300 ppi) to compare them.
The issue with sending 200PPI to the printer is that the printer driver will still do an up-sampling, behind your back, to the native printer resolution, and doesn't allow to do additional output sharpening at that stage. What that native printer resolution is, depends on the printer brand, and print driver settings. It's usually 300/600PPI for e.g. Canon and HP printers, and 360/720PPI for Epson printers. The printer driver's resampling algorithm delivers relatively low quality, so you're usually much better off doing it yourself.
If given a choice between printing at 200 ppi vs. upres-ing and downsampling to the desired dimensions at 300 ppi, which would you go for? (This is for a friend who has her heart set on a large print of this particular photo).
Definitely go for 300PPI if that's the printer driver requirement, but you can get better quality by using something like Photozoom at 600PPI (if that is the native printer resolution).
I am also curious to know your sharpening workflow with upres-ing. I do capture sharpening in LR4 and then additional (output) sharpening in PS using Smart Sharpen, or progressive sharpening...
Assuming you do a proper Capture sharpening, that's okay. It should only
compensate for lens and sensor+demosaicing blur, nothing else. When you exaggerate things here, it will create artifacts that will only become bigger and more noticeable on enlarged output.
Is there any utility to sharpening before upres-ing?
Be very careful here. You are best off leaving it to proper Capture sharpening, and some Creative 'sharpening' (more of a spatial frequency based local contrast enhancement) at the pre-enlargement stage. LR doesn't offer as much choice for postprocessing your output file as e.g. Photoshop or other photo-editors.
Topaz Labs does offer some possibilities to use their filters outside of Photoshop, and use adjustment layers for increased control, via their photoFXlab utility. They also offer some plugins to increase and/or manipulate resolution (called Infocus) and detail (called Detail, which also offers basic deconvolution sharpening).
Make sure to check out PhotoZoom Pro, because I estimate it will give you the most benefits for the particular print scenario that you outlined.
Another application that should not go unmentioned, is Qimage Ultimate. It's a Windows application for generating very good quality output, because it automatically does the upsampling for you with superior algorithms, and uses an adjustable automatic output sharpening algorithm (called DFS, or Deep Focus Sharpening) that does not create halos. Qimage does have a bit of a learning curve if you really want to benefit from its many capabilities.