I too have been investigating this (the site I’m helping build will be selling mostly paintings from local art galleries) so specifying item weight simply isn’t enough to get accurate shipping estimates to appear for a customer while shopping online.
I have found a Dimensional Shipping extension from this website: http://www.webshopapps.com
However, I am not yet sure if it will work for me. I believe the dimensional thing works best with things that have already been packaged and the dimensions and weight you enter are of an already packaged item, so it doesn’t appear capable of calculating the cost of having something packaged by, say, a UPS store (which is required in order for them to honor their insurance; you can’t pack it yourself and then take it to them).
I sent the company an email asking about this and they’ve not responded yet. The extension looks like just what we need but it looks like I might have to purchase a separate extension just to separate handling (packaging) costs.