If you can't find a viable way to offer 'free' shipping, then the next best user experience is to offer full disclosure as early in the buying process as possible. (Note - we put 'free' in quotes since, of course, shipping is never free ... but sometimes the cost is not passed on directly to the consumer!)
The first page on an online store where the cost of shipping becomes interesting is on the product page. Please, follow our advice, and work hard to display your shipping costs. If you are offering fixed rate shipping, then find a nice corner for a banner. If you're using real-time shipping rates, then please note that AspDotNetStorefront 9.5 lets you showcase the shipping estimator on the product page.