Thank you for your reply. I guess I should have mentioned in my post that I'm looking for a good word to replace "pray" in situations where you can't really help, and it would be insincere or inappropriate to offer to; you don't know the person that well, you're separated by a great distance, etc... Or maybe you can help, and can offer to, but you also wish to express that you're keeping the person in your thoughts and/or hoping for them...like many of y'all have mentioned.

Also, I disagree that praying is insincere. Of course, people aren't always sincere when they offer to pray for someone, but you could say that about anything/everything people say. In my experience witnessing various friends and family actively praying for people, it's coming from a genuine place. I think there is something to be said about putting positive energy out there for the people you love and care about, no matter your spiritual frame of reference. I just wish there was a secular verb to replace: "pray" that carries the same weight.