While researching an idea for a blog post, I came across a story about a little girl named Meredith whose beloved dog Abbey had died. Meredith was so concerned about what would happen to Abbey that she asked her mother if she could write to God and ask him to take special care of the dog. Meredith's mom helped her write the letter, address it to "God/Heaven," and mail it (with multiple stamps, because "it may take lots of stamps to get a letter all the way to heaven"). Some kind person at the US Postal Service read Meredith's letter and sent her a very sweet reply (signed "God, and the special angel who wrote this after God told her the words") and a copy of the book When A Pet Dies by Fred Rogers (of "Mister Rogers' Neighborhood" fame). According to Snopes.com, the story is true; it happened in San Antonio, Texas in 2006.
I sometimes envy believers when it comes to offering words of comfort to mourners. Even if prayer has no demonstrable effect on the world, the phrase "I'll pray for you" has an emotional effect on believers. Even prominent atheist Christopher Hitchens, who has esophageal cancer, has said that he appreciates the intent of those who pray for his recovery even though he urges believers not to "trouble deaf heaven with your bootless cries". If somebody (especially a child) asked me if the soul of someone they loved was in heaven, it would be difficult, if not impossible, for me to be blunt and say "no." I'm faithless, but I'm not heartless. I think the best I could manage would be something like "Wouldn't it be nice if s/he was in heaven?" But then I'd try to turn the conversation to "What would s/he do in heaven if s/he had the choice? What kinds of things did s/he like to do with you? I'm sorry s/he's gone, but I'm glad you two got to know each other." If I'd known the deceased myself, I'd try to share a happy or funny anecdote.
Offering condolences as a non-believer requires more work than just saying "I'll pray," but if "I'm so sorry for your loss" doesn't feel sufficient, there are ways to comfort without invoking religion. Sadly, as I and my family and acquaintances get older, I'm going to have all too many opportunities to practice this skill.
H/T to Michael Josephson, Founder of Josephson Institute