Thanks for all your suggestions, but alas, no luck.
Joel: I went through all those steps and the only result was that they made my text a slightly different color. Also, it seems that that option will always make a callout, I just want a box.
MFarmer: Nope, that's for labelling features. I already have the text objects, just need to have a box around them. In fact... I already have the boxes (see below)
Paul: I can't find that option, I have ArcEditor 10.0, is it a new option, or on a higher license level?
So to give a bit of background, I've been asked to export data from this map (Illustrator/MAPublisher) back to Arc.
Most of it is working just fine, except road numbers, junction and exit names etc. I've exported the text as mid/mif and converted them to Geodatabase annotations using FME, the boxes themselves are exported as shapefiles. But in order to make that work in Arc you need to have exactly the same font and settings as in Illustrator, and there's no way we can guarantee that for an external client. I've tried adding the text as an attribute to the box then use labelling in Arc, which actually works okay unless it's a multi-line label, the standard labelling engine doesn't seem to want to do that. I don't have Maplex unfortunately.
Oh, and we're talking about almost 1100 of these all across the map, so if we can avoid redoing all of them manually, that'd be super.