Awkward moments are AWESOME!
No, really, they're lots of fun. Why? Because they are funny and a great opportunity to show a girl you can handle pressure. Lots of guys buckle under the pressure and try to hastily fill the void, often making themselves look visibly uncomfortable.
That's the opposite of what you should do. Rather, you should enjoy the moment and remain calm, then try one of three methods to move past the awkwardness and toward a more intimate moment with her.