If you can do them, agility exercises will strengthen the ankle -
plus train to do sudden stops, starts and changes in direction.
The reason I say "if you can do them" is that they will put way more stress on the ankle than passive exercises like the ones Povl Carstensen recommends above, and ones to start with after an injury.
But if you can do these agility drills in a controlled session, when you get into a tennis match, your whole body can move in a coordinated fashion to minimize the stress on the ankles.
USTA agiltiy drills: http://www.fhsgirlstennis.com/info/U...t_Training.pdf
And you don't have to do these agility drills on the tennis court - they can be done in a gym, playing field or even your back yard.