Thank you for your reply.

What kind of fallback? 

I want to detect if char is visible and use a different one. E. g. bulb can be replaced with "!". 
 
IOW, what did you intend to do if you find out
that the font configured by the user does NOT have a glyph for the
character in question?

Yes.
 
I'm asking because some fallbacks don't need to know whether a
particular font can display a particular character.  But I'm not sure
those fallbacks are appropriate for your use case.

> I tried to use char-displayable-p but it seems like it is not
> what I am looking for.

I believe you want font-get-glyphs.

I will try that out. I am not sure what FONT-OBJECT parameter stands for?

Thanks,
Ivan