My monitor's native resolution is the same, 1680x1050.
The game's native res is (IIRC) 1024x768 - a 4:3 aspect ratio, as it was not built to run in a widescreen format.
There are various "fixes" out there to specify a different resolution, including running the game in a widescreen format. Check the SH3 Mods Workshop Forum, there may be a stickied thread there for widescreen mods or you can search the forum for "widescreen" and see what comes up.
Personally I have not experimented with any of the widescreen mods, as the last time I checked none of them were designed to "fit" my monitor's native res and aspect ratio. It's been a while though, so things may have changed so have a look as noted above.
What I use is the Res_Fix mod, which (once installed) allows you to specify the resolution of your choice for the game when it runs.
http://www.subsim.com/radioroom/down...o=file&id=1092
You can specify 1680x1050, but without modifying the graphics to fit a widescreen format you will probably see some stretching of images in the 2D bits of the game (what would normally be a round dial will become an oval shape, for instance). Some users aren't bothered by this, for some the effects might not be as great - your mileage may vary.
I didn't like the stretching effect so I set the res at 1400x1050 and turned off auto-scaling on my gfx card, so the game runs fullscreen but without being stretched out to fill the available 1680 horizontal space - instead I get narrow black bands down each side, kind of like horizontal letterboxing. (I have an ATI Radeon HD4650, if you have the Catalyst Control Center for your gfx card, that's where I went to turn off auto-scaling.)
So in short (I know, too late for that) it is possible to run the game at 1680x1050 with the proper modifications. You'll just have to try some things out and see what works and what looks good to you.