The above site looks nice as well, but you can check out this site too if you want http://www.tennis-warehouse.com/catpage-FITNESS.html
These braces are for tennis players with weak/injured ankles. If you have ever played tennis, you know that rolling ankles can be rather common and is a major concern. The bottoms are soft and thin for the most part because you are supposed to wear them in shoes. I imagine they would be fine on the mat as well. A lot of tennis pros use the lace up ones (I would suggest you check out the ASO one) or just tape their ankles up nice. Either way, look for one that gives good lateral support to help prevent ankle roll, so look for something geared towards tennis or basketball. Both require lateral movement, with tennis being more so, and the lateral movement is what is going to increase the chance of rolling. Perhaps our aikiweb nurse will pop in and give you a good suggestion as well.
I have a weak ankle and usually my neoprene one is enough to get me by. Make sure you are resting and don't push the ankle too hard. I severely sprained mine a few years ago and was stupid and never went to the doctor. Hence, no rest, no crutches, etc. I paid for it for several years and my ankle has never really recovered. Take it nice and slow!