Place a cotton cloth directly over the stain and with a dry iron (NO STEAM!) press down for several seconds on the cloth. Remove and check the stain. Keep doing until the watermarks are completely gone. It could take a minute or two to get the stain out completely.
Dollhouse says, I did this technique on my husband's great, great grandfather's dining room table and removed some pretty big and deep white watermarks.
This has us feeling hopeful about our fireplace mantle, which looks like it's been through too many cocktail parties without any protection. (thanks, dollhouse!)