Use V.A.T.S. to Take Out Grenades & Other Objects
If you're deep into the game, you might have discovered this already. If not, allow us to explain.
The V.A.T.S. system allows you to slow down time and target specific parts of an enemy. The game explains this mechanic early on. What it doesn't tell you though is that you can actually target objects enemies throw at you.
For instance, if you use V.A.T.S. and toggle, you can actually toggle to a grenade or anything else that's coming your way. You can also use the system to target mines in the distance.