You could bend the 22nd fret up a whole step. You could use a slide, ring, maybe even a fingernail to "fret" it in approximately the right place (compression or distortion would help and you should use vibrato to hide the inevitably poor intonation). You can try sliding the first string down off the edge of the fret board so it both stretches and "frets" against the side of the fretboard and see what note you get - it might be close. And my last idea is push it down against the neck pickup and maybe bend it to try to get it in tune.
The first one (bending the 22nd fret up) is the only that you can be sure will work and that will give you solid control over the intonation. The rest are just tricks of dubious value - but I thought I'd throw in every idea I had.
My solution to this problem was to troll music stores for used guitars with 24 fret necks and floyd rose tremolos, which eventually yielded a great deal on a guitar that turned out to be pretty good for the price after a little work.
Oh yeah, Dom's answer about harmonics is a good one, although you want the 5th fret which is two octaves higher than open, not the 12th.