If you don't mind the reduction in quality, you can just Scale them up until they fill the screen.
Yea, tried that, and thought the (rather high) reduction in quality must have been something I was setting wrong. Really...no better way?
The rule of thumb with scaling is always go down, never up.
Meaning edit and deliver at widescreen standard definition, rather then high definition.
Yes, there are better ways, but not for free, and it isn't perfect.
There are software programs designd to uprez SD to HD. Some do a reasonably decent job, but not great.
But the question is, do you really want to do that? You might find that Jim's suggestion of editing the whole thing in a standard definition frame size will allow you to play back at high quality at less than full screen if you want, or go full screen using hardware to uprez it, and get a better result, but less quality than the smaller image.
You can try this one - it has a free trial - http://www.videoconverterfactory.com/tips/sd-video-to-hd-video.html
There are others, just use Google to find them.