When I hit the nut flush I continue my betting. I'm hoping that my villain just hit the flush and decided to raise me. If I get raised I generally think about it for a moment then call then check the river to induce a bet.

I don't like to stop the betting because I want as much $$ in the pot as possible. If I check the nuts on the turn, there goes a lost opportunity and by the river my villain may not have may his hand. A value bet on the river after checking it through may not even be worth the call.