What do you say when you don't know what to say?

A family I know and have been close to for years recently lost their grandfather. And there is a bit of tension in the family because a far-away grandchild (not someone I know personally, but a grandchild in another unit of the family) did not call or reach out to the family in any way after the death. Her reason: she didn't know what to say.

Now, you don't have to read much of my blog to guess what I think of that.

But I do have compassion for her position. I've been near to people in grief and not had a clue what to say to them. My operating theory has generally been to just call or stop by and stumble my way through the conversation. I guess, I figure saying something awkward is better than not saying anything at all.

I realize this is far from ideal, however. Does anyone else have better advice for what to say when someone is feeling loss and you have no idea how to express your sympathy?