I usually award XP at the end of a session (unless it ended in the middle of something big, like a cliffhanger), but. . .
I use the "general downtime" variant from the DMG, where you have to spend at least 1 day per character level you're going to in non-adventuring, non-healing, non-spellcasting/spell-research tasks (training, resting, vacationing ect.), and then they have to generally be some place where they can spend that time in relative safety (no place in a dungeon counts as "relative safety", but a viliage, large friendly army camp or fortress would be just fine.
So, XP at the end of sessions, but you can't do much with it (besides cast spells and make items) unless you can get to a place where you can spend a few days (or a couple of weeks) resting/training/practicing.