Have a large drink yourself. I slept right through last night.
Lol! On a similar lighthearted vein, I was about to say phenargan!
Seriously though, if she has a tendency to be a little wakeful the night before big events it is unrealistic to think there is anything that will stop that before the 11+. Obviously follow all the basics, relax a while, warm bath, calm story etc etc, but then I just wouldn't add to the stress by worrying about it. The 11+ is generally associated with a little nervous excitement! Believe me, she will be shored up by adrenaline on the day. And actually, the kind of laughing excitement you get when you and all your mates are 'in it together' kind of camaraderie. Honestly, lack of sleep won't be an issue until the meltdown you must expect at 4pm that afternoon, when you ask her to put her late in the dishwasher!