How do you appraise original art?

Katherine and I bought some art for a fraction of the published price the artist was showing. We met with the artist and like him a lot. We believe he is sincere in saying this are orginial pieces and that most of his stuff goes through his agent for the published prices. We love the art so the value is not very important, but how do we know what the real markt values are? And what do you do about insuring them (if anything)? we are new to this. Thanks.

 

Very helpful; thanks.