I have a vector image that I'm trying to export for an area of a web page that's 200x300 pixels. When I export it, the quality of the image is significantly reduced. Is there a way to fix this?
Of course you loose "crispness" in fact you limit a lot the information you can have on an image so tiny.
You do not "loose" crispness in a pdf file because pdf is still a vector file, so if you zoom in you still have full detail on text.
You can not avoid that. But there is a little bit you can do to improve it.
Try exporting at double size 400x600 and resampling the image using gimp. After resampling apply some sharpness.
But perhaphs you simply have too much text on the tiny image. Try to optimize that. If it is a banner for example optimize your information.