Alot of people recommend keeping all the artifacts, but I usually check if it's something I'll actually need*, and if not, I'll offer it, because having my evaluation plummet makes me feel uneasy. Although I've heard that as long as you send up a good Einharjar every chapter, your Evaluation won't suffer as much, or something.

Also, alot of artifacts can be used for transmutation (especially when you get the Creation Jewel/Gem later on), so it's worth it to check out if something is worth keeping in an faq or something (if you aren't opposed to that).

*Be sure to keep an artifact called Bark of the Dryad...