Most of the battlemaster maneuvers reference "hit a creature with a (melee) weapon attack", and Greenflame Blade/Booming Blade tell you to make a melee weapon attack as part of your spellcasting action, so it seems those would work just fine.
Two caveats:
- You're not using the Attack action when you cast a cantrip, so you can't use Commander's Strike with GFB/BB ("When you take the Attack action...")
- A maneuver that replaces a melee attack weapon with another effect causes the cantrip to fail; it'd be up to the DM to determine the effect, but I'd rule the replacement effect still occurs, just without the spell effect. (There isn't currently a maneuver that does this, as far as I can tell, but if Commander's Strike didn't have the 'when you take the Attack action' text, it would qualify, since it turns your GFB attack into an attack for an ally, and GFB/BB both state that if you can't take the attack, the spell fails.)
My question would be w/r/t Greenflame Blade and Sweeping Attack -- if you use Sweeping Attack on the GFB attack, would you be prevented from applying the secondary damage from GFB to the second creature you damage with the Sweeping Attack? Based on the description of both effects, I'd say yes.
--
Pauper