What’s the word to describe that I ——— your artwork?

When I see a famous writer, I will say, “Hi, I read your book” (or “have read”?).
When I see a movie star, I will say, “Hey, I watched your movie" (or “have watched”?).
So, when I see a artist, what’s the word in: “Hi, I ——— your artwork”?
(Maybe it’s a photo, or a painting or a sculpture.)

If you're wanting to convey something more positive than "have seen", you might try:

I was very impressed with your artwork.

or, more simply:

I was impressed with your artwork.

(This works especially well if the artist happens to be an impressionist painter who appreciates puns.)

You could also try one of these:

I very much enjoyed your artwork.
I quite enjoyed your artwork.

That has more of the "savoring" connotation that you mentioned in your comment.

One more possibility:

I have admired your artwork.

According to NOAD, admire can mean to regard something "with respect or warm approval", or to "look at with pleasure".

Ordinarily, one would say "I saw your painting". If the piece were more of an installation or somehow involved an element of performance art, one might be better saying "I experienced your work". Can you provide some more context about what you are trying to communicate? Do you just want to get across that you have some familiarity with the artist's work, or are you trying to initiate a deeper interaction? If the latter, you probably want to talk more about your evaluation of the work, or about your subjective experience of the work.