I don't know if I do it right or not, so take my advice with a grain of salt.
What awes you? What books have you read that give you that feeling? Dissect them, look at the pacing, and the introduction of the elements that give you the shivers.
Doing that for myself, I've found that authors who don't overdo things do the best job making me feel it when reading their work.
For example, Smaug in The Hobbit. When I read that story, he inspired awe. I think part of that came from the fact that he was so built up into such a badass dragon, and he was the only dragon in that story. If Tolkien had them get captured by a bunch of draconian-esque humanoids (instead of wood elves) and they were fighting venomous wyverns instead of giant spiders, etc. I think he would have lost a lot of his pizazz.
The other thing I have noticed is the character's reactions. If a character is awed by something, it tends to awe me as well because I'm seeing it through their eyes (hopefully). Patricia McKillip did this really well in her short story, Harrowing the Dragon of Hoarsbreath. I loved the setting in that story.