Peter,

yes - for ONE frame.

if you want to deal with ALL document frames at once - you need script.

OP mentioned he has 90-100 such frames in document. OP knows those "tricks" with KS or double clicks, and he still asks for help here. I insist - he needs a script.

Well, I'm not sure if I'm not hurting the rules of the forum (there is special forum for scripting)...

However, here is the JS code I use for identical purposes, maybe you'll find it helpful:

/*
This script Fits Text Frames to Content
*/
myDialog = app.dialogs.add ({name:"Script going to start",canCancel:true});
 
with (myDialog)
     with (dialogColumns.add())
//     with (dialogRows.add())
     {
                   staticTexts.add ({staticLabel:"This script will Fit Text Frames to Content."});
                   staticTexts.add ({staticLabel:"Proceed?"});
 if (!myDialog.show())
{
     myDialog.destroy();
     exit(0);
}
}
var myTFs = app.activeDocument.textFrames.everyItem().getElements();
    for (var i=0; i<myTFs.length; i++) {
            myTFs[i].fit( FitOptions.FRAME_TO_CONTENT );
            var gb = myTFs[i].geometricBounds;
            while (myTFs[i].overflows) {
                        gb[3]++;
                        gb[2]++;
                        myTFs[i].geometricBounds = gb;
                    }
            }
var _d = app.documents[0];
var _allStories = _d.stories;
for(var n=_allStories.length-1;n>=0;n--){
var _storyAllTextFrames = _allStories[n].textContainers;
for(var m=_storyAllTextFrames.length-1;m>=0;m--){
_storyAllTextFrames[m].select();
            //Fit Frame to Content:
            try{
            app.scriptMenuActions.itemByID(11291).invoke();
                }catch(e){};
            //Deselect All
           try{
           app.scriptMenuActions.itemByID(278).invoke();
                }catch(e){};
            };
        };
 
    alert("Fit Text Frames to Content\nDone!");

Ok, so does anyone have an answer to the original question? which is fitting a frame horizontally? I'd love to know how to do this. It's pretty annoying to have text jump down to the next line when fitting the text frame instead of the frame extending horizontally to fit the text.

No Peter, that's not what I'm asking. I'm simply asking if it's possible to say, increase the point size of the text, then fit the frame and not have the text skip to the next line, but fit it horizontally.

I think I know what the OP means. This can be done with GREP styles. check out this article to see if this helps:

http://colecandoo.wordpress.com/2012/02/18/square-pegs-now-fit-into-ro und-holes/

that's correct, i'd meant to answer Andymc7's question with the link there. oops