A friend of mine recently came across a wooden cup with the image of a
ship burned into it, and the phrase "Kuedja fra Islandi" written
across the base. (Not under the cup, but across the base, where it's
clearly visible.)

I would guess that it means "<something> from Iceland", and my first
thought was that it simply meant "Made in Iceland". :-)

But that doesn't really seem correct. Besides, the prominence of the
words seems to indicate something a little more significant than that.
But we can't find the word "Kuedja" in any source, or any word that
seems to decline that way. Our other thought was that it might be
someone's name.

Any ideas?

Jamie