Many saw players I meet started on the theremin and are able to play both instruments. This is probably because they can have similar sounds, so a person who enjoys the sound of a saw  might enjoy the sound of a theremin. Both instruments take great concentration to play. An exceptional theremin and saw player is Gregoire Blanc. He is a French musician who, according to his website, has been playing theremin since he was 15. In this video, you can see him play a duet with himself on the theremin and saw. He has many interesting projects in the works and if you take a look at his website, you can hear some truly beautiful music.

Here he is playing Passacaglia by Halvorsen.