Great question. Here are a few ideas I picked up over my 32 years of teaching elementary, junior high, and high school band.
The equivalent to the mouthpiece buzz for brass is the optimum mouthpiece input pitch for woodwinds. This should be checked regularly at all levels of playing. (All are Concert Pitches)
soprano clarinet - C, alto clarinet - Ab, bass clarinet - F, Eb contra - Eb, Bb contra - C
soprano sax - C, alto sax - A, tenor sax - G, bari sax - D
It is especially important for saxophones to practice tuning unisons and then octaves in all registers of the instrument. This is best done in pairs with each player taking turns tuning the upper octave once the unison is in tune.
Another silent exercise the woodwinds can do during the warmup while the brass are doing their thing is to practice difficult finger changes. On sax it could be C or C# to D, Ab to Bb (with the side key), Low C to Eb using the rollers etc. Clarinets can always benefit from crossing the break exercises. Later in the year it could be silent fingering of a difficult passage in the music.
The warmup should always include long tones with crescendos and diminuendos AND an amplified tuner to hear a fixed target pitch throughout.
In advanced level bands have the woodwinds play the brass lip slur patterns (by ear) along with them instead of just playing long tones. It is a great way to teach intervals and ear training in all keys.
The real trick to a great warm up is getting the right balance between new and challenging and old and familiar. Too much of one and the warm up takes too much of the rehearsal time with lengthy explanations. Too much of the other and the warm up is "the same old boring thing we play every day".
Good luck. Hope some of this is helpful.