I haven't had a whole lot of time for recording lately, but I've done a bit of experimenting with the uke. I don't have a pickup any of mine so it's acoustic recording for me.
I recently picked up a good deal on one of those Joe Meek JM37 large diaphragm sets that also included the small diaphragm JM27. (I've also got a bunch of other mics of various ages and brands that I haven't played around too much with.) They were the new ones so I used them.
For the most part it's about placement. Normally, I'm kind of a fast and nasty, "put a mic in front of it and go, I'll futz with the EQ later" kind of engineer, but I have to say that taking the time pays off. I usually record dry and flat, preferring to do my voodoo later with reverb and the like, so I can fine tune it without being confined to what got recorded. The track is a clean slate to be enhanced.
Best results for me were having the large diaphragm about a foot and a half away at a slight angle to the soundhole. Kind of pointing towards the 12th fret. You'll have to take some time to kind of shift things around a little bit, but for that particular mic there seemed to be a sweet spot somewhere in there. (I'm sure that it's going to be similar with any large diaphragm.) If it was too direct, it'd hit the red. Too indirect it lost the uke. It also picked up some nice ambience from the room as well which was a bonus. Nice small room sound. But large diaphragms tend to emphasize the high end frequencies. By itself it was kind of brittle and too bright.
To balance it out I put the small diaphragm on a boom and placed it behind me by my head pointing down at about ear level. This one was a little trickier to place, but entirely worth it. It takes a little bit of maneuvering but you want to get the mic in a place where it's picking up essentially the same sound your ears hear when you play, but is pointed in such a way that the pattern isn't picking up your breathing as well. This was the sonic money shot.
Balanced out I ended up with something that sounded pretty much like I normally hear it,sounded pretty natural and I didn't feel like I had to fiddle too much with EQ or even add any reverb since it captured the room sound really well.