Apologies for posting what I fear may be a stupid question, but I haven't been able to find an answer on the boards already.

I'm having my frame stripped and painted, so everything's obviously coming off, including the headset and races. They appear to be in fine condition, so I'd rather not replace them. But I was wondering if there might be some hidden difficulties getting them back on the frame once the paintwork is done.

You'll want to have the mating surfaces of the headtube reamed and faced to clean the paint out. It takes a well-equipped bike shop to do this, but it's straightforward. A good shop will also have a press for reinstalling the headset cups.

I've done this after having a frame and fork powdercoated. It's like a new bike.

Excellent. Cheers!

an experienced bike painter/powder coater, IME (and i've had a few bikes repainted and/or powdercoated) will not allow the paint to enter the headtube to the extent that it will interfere with re-assembly and if any gets in there it should be easily removed with a bit of hand sanding. as for refacing, i've never had to have done to any of my bicycles and most of them have been purchased used and then refurbished.

OTOH, i would make it a point tp ask anyone i considered to repaint a frame/fork, whether or not they had any experience painting a bicycle frame/fork, if they say "no" i let them down gently and move on.

Assuming the cups and races were in good condition before removal and were removed properly, sure, put them back in. If you are having the fork also painted, be careful removing the crown race as these can be difficult to remove without damage.

The framebuilder who's doing the job said he'd charge a nominal fee to take care of it, so I believe I'll just leave things in his capable hands. Thanks, all!