I dont know about buddhist or non buddhist, but I do use something called mindfulness, which is similar to meditation. It does help somewhat. The trick is to do it when you don't need it and practice. Then when anxiety hits, your mind and body are already conditioned to act in a certain way when you begin a mindfulness exercise. Most often, with me anyway, my anxiety is about something that happened in the past and I am reliving it or something that might (or might not) happen in the future. Mindfulness helps to bring me into the present moment, thus away from the past and the future.

There are books you can get on this practice, some of the religious, others not.

I like using the free mindfulness exercises on youtube. Most of them just have you focus on your breath.

Hope this helps you some.

God bless you.