Atheist/agnostic form of expressing condolences

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.?

I find this question somewhat odd, because by far the two most common ways of expressing condolences to someone recently bereaved are in my experience quite secular and non-religious:

Sorry for your loss

– and

My condolences.

In my own, personal experience, both these phrases are much more common when expressing condolences than “You(r family) will be in my prayers” or anything like that. The latter type (whether based in religion or more secular versions as in Nate’s answer below) might well be said after the basic expression of condolences, à la, “I’m so sorry for your loss; you’ll be in my thoughts”—but I have not frequently heard it used on its own.

An appropriate secular substitute for prayers is thoughts.

Your family will be in my thoughts.

It sounds a bit odd if you think about it too hard, but it is a common idiom.

A popular phrase is "I am sorry for your loss".

A variation is "I am saddened by your loss".

This variation should address, as was pointed out in the comments, that sometimes the word "sorry" implies blame.