Instead of waiting until the caster's turn in the round, the player announces the spell to be cast at the top of the round and the action resolves during the PC's round. For NPCs, if their location is known to the party, I will announce at the top of the round (or when the NPC is revealed) that the NPC is casting.
Mechanical consequence is that an attack on the caster during the interim has the potential to disrupt casting (opposed by a Concentration check). This houserule harks back to previous editions of D&D where there was a casting time to be resolved. The concentration check would work as normal.
This would not apply to spells cast as a free action (ex. featherfall).
What applies to PCs also applies to NPCs, so any resulting vulnerability works both ways. Casting spells which are not full-round or longer actions will still permit the caster to move as normal during the round.