Saxophones project their sound through the tone holes and the bell. The most natural pick-up is achieved if a mixture of these two sources reaches the microphone. About 10 to 15 cm above the bell, aiming at the sound holes is a good starting position. An omnidirectional DPA 4006A, 4007 reference mic, 4041 large diaphragm, a cardioid 4011A or a wide cardioid 4015A mic can be used with great success in this application.
Moving to the bell and looking inwards gives a very bright sound and minimizes leakage. Pointing the microphone to the sound holes produces a warm and full sound but also picks up fingering and key noise.
A compact omni 4006C, compact cardioid 4011C or compact wide cardioid 4015C can easily be mounted in a shock mount on a microphone stand. Moving the mic from the side of the bell to the centre gives maximum brightness, but the sound may become too aggressive for certain music types.
The miniature mike DPA 4061 is also worth a try for this application. It can handle 144 dB peak sound levels before clipping. The miniature mics have a slight high frequency boost in the 12 kHz range. Advanced users can remove the protection grid which produces the high frequency boost and a linear and smooth sound is produced, but you must be extremely careful about not touching the exposed diaphragm. Because of the perfect omnidirectionality of the Miniatures the pointing direction is not critical. The DMM0007 self adhesive pads will aid in cleverly affixing the mic to the instrument.
The soprano saxophone (usually a straight model, the curved variety is far less common) could be miked at 10 to 15 cm distance, pointing at the position of the right hand. If fingering noise is too prominent, the distance could be increased and a cardioid 4011A or the compact cardioid model 4011C can be used.
The big challenge with soprano saxes is that the instrument carries two very different sound elements that are both indispensable. At a distance these elements blend together nicely, but when close miking you have to be aware to cover them both or preferably mic them both. You cannot achieve the character from the opposite element by EQ'ing on one of them. Higher frequencies (above 8 kHz) are only directed along the axis of the bell, whereas mids and below are prominent at the tone holes. The two mics should not be equally loud. Start with the one at the tone holes and mix in the bell mic. Pan them just a tiny bit apart from each other.
For live use (or home studio) the 4099S clip mic may well be the ideal solution. The 4099s have a super cardioid polar pattern that allows the mic to focus on the instrument and get a good isolation from the other sound sources on the stage or bad acoustics. This also reduces the risk of feedback significantly, while keeping the rich and nuanced sound of the instrument uncolored. But because of its high directionality some time should be spend on finding the right placement of the mic. The position will always be a compromise trying to capture the whole instrument with a narrow pick up pattern.
On alto and tenor the 4099 should point at the upper part of the bell, catching some from the tube as well. On soprano the 4099 should be mounted on the bell but pointing up almost parallel with the tube.
Remember, the DPA microphone has an off-axis response that has zero phase shift and this is coupled with an on-axis brightness peak on most types. By pointing the brightness peak a little to the side or down, the reception of mechanical sounds (fingers keyboarding) will not be prominent, yet there will still be a balanced clear sound.