I have lived in the U.S. for 20 years now but I am yet to find an elegant and eloquent phrase to express condolences to somebody upon the death of a close one that does not involve religiosity and prayer ("Your family will be in my prayers").
My native language is Bosnian (Serbocroatian) and we simply say "accept my condolences".
Can you offer some examples of similar elegant, eloquent, and SECULAR phrases in English that do not imply God, prayers, religion, heaven, etc.?