If your requirements allow it, you could try to convert the character to outlines first. That will result in a graphic that is maybe easier to control.
>but the frame is reducing beyond that size
No, it's not: the frame is fitted to the character's bounding box, which needn't coincide with the characters visual extremities. Tony's suggestion gets around that, but loses information like baseline, x-height, etc.
What you're seeing is the way the character is designed. It is designed to extrude beyond its bounding box and so it extrudes beyond the fitted frame.
The only way to get the actual extents of the character's glyph is to convert it (or a copy of it) to outlines and then get the geometric or visible bounds of that.
I had tried getting the bounding box according to Windows (outside of InDesign). I could get the exact bounding box, but the units I was receiving didn't match what I was seeing in InDesign. Since both programs are using the same font, I'd expect to get the exact same dimensions.
Converting the character to outlines at least gives me something to run with.
Thanks, all, for your responses.