I make a double back cut for that situation. Back cut the top into the beginning of the face, and then back cut the face. Takes a bit of practice----I learned to leave the top backcut a bit long as it is easier to shorten the top than the face.

You can leave a wafer-thin portion of the miter at the very top of the coped piece, then lay that over the butted piece so it resembles a miter. If you try it, you'll need a real steady hand to cut it and not lose the paper-like tail of wood. Most of us never worry about making base that perfect, because it's just base.
Casey

"Most of us never worry about making base that perfect, because it's just base."

Maybe on paint grade, but stained base needs to be dead on!

You can cut the coping a little strong leaving some material to be filed to get your edge. Takes more time and patience, but you'll get a nice joint.

I obviously did a poor job explaining what I meant, which was this: regular workmanlike coping is adequate for baseboards, and leaving the miter tip at the peak is probably overkill. Such detail is best left for piano cases and jewelry boxes.
I'm not advocating sloppy work.
Casey

Thanks for all your advice!

I was hoping there was an easier way, but I guess I will have to be patient and work with what I've got :P.

Sorry for my misunderstandin', Casey. I need to sharpen my pencil!