There are some 3rd party plug-ins that can help but a pixel is a pixel. If you scale to 200% you're making 4 pixels out of 1 so things are going to get soft.
Before I reccomend a plug-in tell me a bit more about your system. Win? Mac? What aversion of AE? What type of footage (MPEG - DSLR - XDCam???).
Have you been watching too much CSI? You'd be better off doing this in 720p and then you can "zoom" into your 1080p footage a little bit. You could apply a little sharpening to the zoomed clip, but don't expect miracles.
And zooming something in AE will produce no better results than Premiere.
One possible solution would be to output an image sequence, then batch process through Photoshop and Genuine Fractals (which claims to increase resolution will less visible artifacts than usual bicubic scaling most apps use)
There's also Instant HD from Red Giant. My experience has been mixed with it. Download the demo and see if it works for you before buying it.
@Rick Gerard: I am on Windows 7 64 bit, using AE CS5.5, but have never used it before. As said above, I use Sony Vegas but have heard that AE is good at improving footage. My footage is from a video game, recorded with FRAPS, and rendered in MP4.
@Navarro Parker: Will it not decrease quality, doing 720p with 1080 footage? What is the difference between 720p and 1080p, is it the resolution?
I have tried sharpening, but it doesn't help.
How do you define quality? If it's just based on resolution, then yes. 1280x720 is smaller than 1920x1080.
But consider what the target is for your final movie. Is it YouTube? A blu-ray disc? A movie theater?
Putting a 1080p layer in a 720p comp gives you the ability to "zoom" and crop a 1080p layer to a certain degress without the scaling artifacts of enlarging over 100%.