I have lived in the U.S. 20 years now but I am yet to find an elegant and eloquent wording 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 wording in English that does not imply God, prayers, religion, heaven, etc.?