Lyxen
Great Old One
We give inspiration at the end of the game: one given out by the players, and one given by the DM. We also have a cap of three inspiration rather than just one.
I have a checklist of things to do at the start of the game, one of which is awarding the DM's inspiration to a player for what he did during the previous game. I try to fill it during a session, otherwise I give it based on what I remember of the session.