Sometimes long notes wobble a bit. The tone gets a little quiver.
There is a simple mental trick I use that helps with this. I imagine my sustained note as moving forward from my bell through the space in front of me.
It’s almost as if my sound is a column of light moving forward from the bell. In fact, I sometimes like to visualize an entire phrase as a single, unbroken column of light that changes color for the different notes of the phrase.
In lessons, I sometimes use a hand motion where I begin with my hand close to the bell and then, as the student sustains the note, I move my hand slowly away from the bell, giving them a visual image of forward motion to the sound. This often helps.
Playing any note without a sense of forward motion is often a source of trouble. Not only is the note less musically satisfying, the tone is often less resonant as well.
In that way, you can almost imagine a little, nearly imperceptible crescendo as you sustain the note.
When buzzing, it is nice to get visual feedback of the air-in-motion. A pinwheel is good for this. So is a piece of tissue paper suspended in front of the mouthpiece.
Think of this analogy: If you were to drink from a stream, it is better to drink from flowing water…
..than it is to drink from stagnant water!