I've experienced an emotion I think is awe but generally only in response to the physical presence of something in the natural world rather than to sitting and thinking. Being on top of a mountain at sunrise, staring at the sky on a clear night, being up close to a large and potentially dangerous animal and other such experiences have produced the emotion but it is only evoked weakly if at all by sitting and contemplating the universe.

I don't think I have a very firm grip on the varieties of 'religious' experience. I am not really clear on the distinction between awe and wonder for example though I believe they are considered separate emotions.