With the saxophone, the sound is fairly well distributed between the finger holes and the bell. Miking close to the finger holes will result in key noise.
The soprano sax must be considered separately because its bell does not curve upward. This means that, unlike all other saxophones, placing a microphone toward the middle of the instrument will not pick-up the sound from the key holes and the bell simultaneously.
The saxophone has sound characteristics similar to the human voice. Thus, a shaped response microphone designed for voice works well.