I know it is awkward. I remember feeling the same way. I've had others tell me they don't want to make me cry, that it is hard to know the right words to say. My brain can comprehend the fear, but my heart can't grasp the reasoning. If you have a friend, or even an aquaintance, going through the grieving process, don't say nothing.
First of all, there is no "right" thing to say, like there exists the perfect, magical phrase that will make the pain go away, or at least serve some higher purpose. And because everyone grieves differently, I can't say with certainty what any one person might desire to hear. But silence can be as painful as the worst, most insensitive comment.
Silence gives the impression that my pain doesn't matter. It makes me feel like your desire for comfortable conversation is more important than my life-shattering trial. And as much as I long for easy-breezy interaction, my heart won't allow it if you can't even acknowledge the bludgeoning my soul took with this death.
It doesn't have to be the first thing you say to me. It might not be the right moment, but don't ignore the trial altogether. A simple "I'm so sorry for your loss . . . I've been thinking and praying for you . . . Is there anything I can do?" is more than adequate. And don't worry about making me cry, knowing you care enough to talk to me about our trial makes up for any smeared mascara that may result.