For many years I have used a pair of stoneware mugs for my tea -- big (slightly more than 16 ounces), heavy mugs from Colonial Williamsburg. Mine were the middle one in this photo:
I say "were" because today, through a combination of clumsiness and an unstable table, one of them fell to the deck and broke into several thick, heavy pieces.
Oh, well.
There are plenty of them available at Ebay, and I may pick up a replacement, but I'm also thinking of other possible alternatives.