I frequently play lead tenor in a big band, when I'm on flute I find that as long as I'm in the upper registers the flute can cut through the brass & the sound gets out. When I get on the lower end, I use a Shure 58 that is on a stand sitting to my right, there is an on/off switch, & I just have to lean into it. Previous comments are correct in that you have to be close enough to almost touching the mic. I do have the advantage of the lead tenor seat which means there is no one seated on my right side, allowing me a bit more room for the mic stand, when I was playing alto I used a boom stand that stood in front of the music stand & again I would turn it on, lower it toward me & lean in just a bit.
A Shure 58, mic cord & boom stand are extremely affordable!