Jagged edges are a result of anti-aliasing, resampling and interpolation (yeah they are essentially the same)
If you take a raster image (a scan) and increase the size by 200%, then the software has to "guess" what colour pixels to insert to make up the image. It just averages the surrounding pixels so it makes sharp edges blurry and smooth gradients blocky.
All you can do is scan it at an insane resolution or use special spline algortihms to better interpolate the image. But even these don't produce brilliant results.
If you have photoshop/illustrator and a few hours you can recreate the logo in vector format - then you can resize it as much as you want and lose no detail. Requires patience though, my company charge 45 quid an hour for someone (me) to sit and do that
Edit: what zumo said