One you've bookmarked a specific link (which you can copy from www.web2tile.com) and saved it to your favourites list, just call up the web page you want to pin. Rather than pin the site, you open that earlier specified link from the favourites list. You'll be presented with an intermediate web page featuring the favourite icon scaled up.
Here's a demo of Web2Tile in action.
It's not perfect - your target site needs to have a favicon correctly set up, and some websites won't load up in the intermediate page, but it's a free service that's worth playing around with if pinning sites is your thing.