With bitmap formats like GIF and JPG, you're basically saying, "These are the dots I've got", locking yourself into a particular resolution. And of course, your printer has a lot more resolution than the screen, so when you print, it will look lousy.
The best you could do is use a huge desktop, like 1600x1200 (whether it's legible or not, as long as your monitor can handle it), maximize the window, zoom in the page and/or scale the WordArt as big as you can get it, and PrintScreen that.
You really need a vector format like EPS or SVG, not that it would be easy to get WordArt into either of those. What exactly are you trying to do? Why can't you use WordArt?
Frontpage (at least Frontpage 2002/XP) does have WordArt. My wife uses it all the time on the sites she creates. If you go to the View menu at the top and then to toolbars you should see the wordart toolbar. If not, you may not have installed it. To recap