Yes. In fact that is done by default by the code on the page generated by the checkout wizard. Any time the shipping information changes the cart is updated to reflect new shipping charges.
Your friends over here at WebAssist! These Dreamweaver extensions will assist you in building unlimited, custom websites.
These out-of-the-box solutions provide you proven, tested applications that can be up and running now. Build a store, a gallery, or a web-based email solution.