I'd be tempted to implement it as a single-cell Table, although as an imported object, there would be other options.
I don't know if FM11 had the Paragraph Designer » Font » Background feature (or the equivalent in Character Designer), but even if it does, that doesn't provide much control over the box extents, and none over border.
That did it. Added an anchored frame at insertion point. Added a text frame and inside a one-cell table with 100% yellow shading and thin borders on the outside.
Ah, the old Table inside a Table limitation. As long as you're using an Anchored Frame anyway, you could just use it for the background & borders, and put either Graphic Text or an ordinary Text Frame inside it. An ordinary TF would allow using tagged text, Xref, Variable, etc.
The FM version and output workflow (print, PDF, HTML, etc.) might dictate what's ideal, particularly if you want any vector elements in the final rendering to be SVG.