OP here. Just wanted to follow-up and let you know the resolution in this case. I called customer service and explained that one of the passengers passed away prior to the flight, and I asked what was the process for a refund. The agent was incredibly kind and said how sorry she was regarding the situation. She said she would go ahead and process the refund back to my credit card for both tickets (for the deceased and for the person accompanying the deceased). She did not ask for a death certificate, although I was prepared to provide one if needed. I'm so impressed with Southwest's customer service!