If the curve radius is not too small, normal text with unaltered characters might look ok.

Some vector graphics software allows you to deform objects to conform to a path. Text can easily be transformed to editable path objects.

Example in Inkscape:

https://graphicdesign.stackexchange.com/questions/103080/ink...

Create text in higher resolution, rasterize it, warp it would be my process, if I needed to curve the characters themselves too. In case I didn't, because the shape is not that small compared to the text, simply wrapping around the shape works. Usually there's a tool to create a path, and then text can go along that path, as if the path were its baseline.

Yea, that’s what I first thought. “Surely, designers encounter this situation all the time and they already do this!?!?” I guess not.