Two things helped my D (now 17) with this. One was in middle school; she took the SAT as part of the Midwest Academic Talent search, and we sent the scores to CTY as well in case she wanted to attend there later. She received an invitation to join an online community called Cogito that CTY helps run -- and that is where she finally found her tribe. She was SO thrilled to finally have friends like herself, even if only through a virtual setting. For a couple of years she spent tons of time online with them, and made one "in real life" friend in town from the group as well. Eventually in high school she stopped spending time there, but just this week she mentioned that they all had a little "online reunion" recently.
The other thing that was huge for my kid was attending Davidson THINK. Especially her second year, where she came out of it with a couple of very close friends. She and one friend have weekly standing Sunday night phone calls that they have kept up for almost two years now. I know that he is one of the few people who gets her and can "keep up with her".
She does have friends in school and her activities. Quiz Bowl, Robotics, school creative writing club, and fencing are all places where she has found kids who are more similar to her than she finds in the normal classroom. So middle school and high school can start to offer some opportunities that are harder to find for younger kids.
