I have found the following exercize quite useful recently - its one of those that can be played by beginners to experts, although newer players should not go higher than their normal range - no straining.
Play long notes on C (mid stave), B, Bb etc down to F#. Strive to get a big resonant sound. Then repeat from low C to F#. Then without moving the mp, repeat from high C. Then repeat the low register again and check the sound you are making is as resonant as the first time. The idea is to check that the sound you get in each register is not effected by the other registers (so its important not to take the mouthpice away at any point - for this reason breathe thru the nose).
Hope this is useful - I found it was. We often play chromatics or scales but how often do we check for resonance in this way?