I say keeping you close in my thoughts and my heart. I like sending love and light, too.

What if you are thinking of them and don’t have a another word for prayers to show sincerity?

Probably "Best Wishes"

Depends on if loss was accidental malicious or if was caused by a long suffering.

“You are in my loving thoughts” is what I sometimes say. Best not to leave it to the grieving person to assign helping tasks. You know what they need—help with pet care, running errands, grocery shopping, picking kids up from school, rides to medical appointments, etc. Just say, “This must be a difficult time for you. May I help by ...”

If they're going through or recovering from a medical procedure, "I hope [it] goes as quickly and as painlessly as possible." For deceased loved ones I offer my condolences.

I offer condolences and then do what I can to change the situation

We don't offer words, we offer action.

I tell them that I am glad they knew love and hope they find peace.

I say. "What can I do to help you?" If local I offer to help with anything I can help with. A friend clear across country I ordered food from Amazon and a stuffed bear for them. Dont offer empty ideas. Do something.

People rarely offer to pray for me, maybe they think it's opening a door to (church lady voice) SATAN. When it happens, I acknowledge they're wishing me well...or maybe they're trying to justify their own delusions and validate their mythology by converting me.

I'll often tell people, I wish you the best or I hope you win the lottery.

Good question. I despise seeing that crap all over Facebook. I agree with you. Just something they say. How many of those folks actually stop what they're doing and pray?? Or, they use that little prayer hands emoticon. Yea that's thought provoking and profound.
Like that one church shooting last year. Immediately all over social media, people were sending their thoughts and prayers about the CHURCH shooting. Really?? Thoughts and prayers didn't exactly help there, did it??
Just empty words.......

They don't. They try & DO something!

" I am sorry for your loss". Specifically for your example.

A phrase I hate even more, that many TV news people use, is "Our hearts go out to you"--because it seems like an insincere cliche. You could just say "my thoughts are with you"...?

I usually just say "Peace and Blessings" or "I'll send you some good vibes" or something like that.

We actually DO something

If it's a relative or close friend, I will tell them "I’m sorry you’re suffering right now, but I’m here with you and willing to help any way I can."

I don't say this but I heard someone else say " Life and death are one string". It helps me. I also heard someone say "When you die you really just move over and make room for someone else."
Sorry I changed the subject (:>

They try to find a solution to the problem. Praying is just a way to do nothing and still feel good about yourself. If it is the loss of a loved one you give condolences and offer them your help in coping.

We say I'm sorry for your trouble...that spares us having to mention anything religious in nature.

Thoughts and wishes.

When my father died I felt like the condolences were virtually meaningless as they changed nothing, but given that my assumption of death is it is probably the same as before we were alive, and in my opinion not existing sounds profoundly peaceful in contrast to the stuggle of life... I would just suggest that they are at peace.

I just don't know what I would say. Guess that's why I'm agnostic lol.

"I'll be thinking of you ."