I've grinded up to 250 skill now in Archaeology, and have yet to see a single "rare" artifact pop-up in my archaeology list. Do these require a specific skill or are they just totally random and you could get one on your second artifact?
The rare artifacts (which make a rare or epic item) are mostly toys and/or for aesthetic purposes, however some are Bind on Account weapons and armor that do not scale like heirlooms. You can only solve these artifacts once per character.
I've seen people say they got the rare artifact at level 80, but to me it seems completely random.
They require a certain skill level to acquire. It's completely random with regard to whether or not they do actually pop up.
That has a complete list of what skill level is required for each rare. I personally got the raptor skeleton mount and pet before hitting 300.