Sometimes a lot of words aren't needed. Be there and support her. Be an active listener and provide words of encouragement. Try to think about all the good things her mother brought into your lives. And make sure you take care of yourself as well. I know how hard losses like this can be. Wishing you and your family the best.

What helped me during these times was talking about something else as a distraction. When I was alone with my thoughts I would go through that heart breaking grief. Time away from those thoughts were always appreciated. I am truly sorry for your family's loss.

Don't try to tell her anything. Just listen. Be understanding. There really aren't any appropriate words at a time like this anyway.

What you have told us here sound wonderful. Your grandmother sounds like a marvelous individual who will remain in your memories forever.

My wife passed away several months ago and I still grieve for her. Grieving isn't something you do once and then It's over. It lasts as new events and things you come across trigger memories. I'm been surprised at times what funny little things bring up memories of her. I have a therapist who encouraged me to think of these memories as gems of her life as they emerge and I have written some of them down in a journal. Each one is a part of what her life with me meant. Special moments of enjoyment of our life together. I will always miss her and her memory will always stay with me as I continue to live my life.

I wish you both peace and love, and offer my condolences on your loss.

Tell her that your grandmother positively influenced the thoughts and actions of many people. So long as those people pass on the positive beliefs, attitudes and behaviors to others, the impact of your grandmother is not gone in an important sense. Physically she is gone, but he memories and influences she left remain with us.

I have seen in another the conflict between the emotional need for comfort seen by some in religion and the intellectual understanding of the finality of death. Only your mother can decide for herself which path she will follow. Affirm her decisions.

I have supported one person on his own journey into theism under similar circumstances.

I know it sounds trite, but I wish you all the very best in your efforts.

This is a clip of Neil de Grasse Tyson talking to Larry King about death.

I am going to assume your grandmother was a good woman/mom/friend and she likely lived a long life. What would she have considered her purpose? For women of the generation I"m guessing your grandmother was it was to be a good mom/wife/friend/citizen. That you're asking for your mom tells me grandma raised good daughters and influenced you as well. Also, if we lived forever as Neil says, we'd have no reason to do it today when tomorrow is always available. And as we don't live forever we wear out and we pass on. But the lives your grandmother touched and inspired will live for generations. Personally I don't fear death at old age. I fear premature death and I think I'm reaching the age where it would no longer premature. What I really fear is suffering. I want a good, clean, non suffering death when I'm old, frail, and broke.

Tell her you love her, and will always be there if she needs to talk.

Your mother will get through this. There's nothing you can do. I wish there was. Sorry about your grandmother.

It's obvious you're grieving as well and that your grandmother was a treasure. As many others have said listening is often the greatest gift you can give the bereaved.

I believe the memories our loved ones leave us comfort us in our time of need and that they live forever in our minds. Dwelling on those treasures has always helped me and I hope will help your mother and yourself.

You can be very supportive without bringing any religion into it. If someone is sick you do not tell them that god will look after them after all.

Oh I can say is I'm sorry about the loss, both of my parents died my mom in 2002 my dad within a year mainly because of loneliness in my opinion, I've always taken comfort in the fact that they are still alive in my mind as long as my memory tracks stay intact they will be there for what it's worth, stay strong help your mom. And a virtual hug to you.

Let see, "I love you. I'm sorry for your loss. I know you'll miss her so much. I'm here for you if you need or just want to talk. Sometime, when you're up for it, I would like you to tell me more about her."

keep it simple and offer ur genuine condolences

a smile and a hand touch too perhaps

How about asking your mother about her favorite memories of your grandmother....

You got this.
Just be gentle with her and yourself.

Stay connected with your mother, she needs you right now and you need her. Both of you can get though this together.

There is a poem on my profile page that has helped me with the loss of my most beloved dogs. It may put things in an eternal light....so to speak. I hope it helps you.

Carl Sagan's wife, Ann Druyan spoke beautifully how she feels about her husband's death, worth the read:
[goodreads.com]

Right now you both need each other. The importance is in being supportive without any mention of non-belief. I'm sure you will chose your words carefully.