BigRichard: I don't think so. You should be able to configure your GPU drivers so that the game is scaled to the monitor with the original aspect ratio (4:3), which would result in black bars on the sides. But it would still be 640x480.
An option, though somewhat tricky, involves FS2. If you own FS2 (or are willing to buy from GOG), you can install FreeSpace Open according to the instructions at
http://www.hard-light.net/forums/index.php?topic=47640.0 . After that you can install FSPort according to instructions at
http://www.hard-light.net/forums/index.php?topic=58357.0 .
FSPort is a mod for FS2/FSO. It ports the ships, missions etc from FS1 to FS2/FSO, thus allowing you to play the FS1 campaign with FS2/FSO. The usual pros of this method are the obvious graphical improvements that FSO makes possible, but in your case there is also a benefit that most people don't even think about: FSO accepts a wide range of resolutions, and has supported widescreen resolutions for a long time. Of course, on widescreen resolutions the interface art and the HUD graphics will distort a bit since they're stretched horizontally, but otherwise it works great. I recommend.
For questions regarding FSO, I'd advise you to visit us at Hard Light Productions.
Every time i download FS2 Open it gets flagged as malware, is there a way to play widescreen without downloading infected 3rd party files