Religion is an integral part of any society. Your characters have to have core beliefs in something (not necessarily a deity or way of life). Fantasy romance authors, along with sci-fi romance authors at times, have a tougher time of creating this. They need to build their religion from scratch, as opposed to paranormal romance authors, who—generally—can use pre-existing religions. However, even if you're going to make your character Catholic (or Buddhist, or a member of a fanatical cult), there are other aspects to this post which you might like to keep in mind.
Aside from the question of Church and organized religion, and the question of a deity, there are other things to consider. For one, what supernatural things does this religion believe in? Ghosts? The Undead? If the latter, is it considered unholy, or just another state of being? What about the afterlife—is there a Heaven and a Hell; or maybe just the fact that your being has risen from the dead is considered to be an afterlife.
Then we turn to more mundane things. Is your character superstitious? If so, many superstitions stem from religion. Let's take a simple one as an example. I'm sure most people reading this have crossed their fingers for good luck at some point. Just the action of crossing your fingers symbolizes Jesus Christ and his sacrifice on the cross. Nowadays, pop culture has taken over the motion and made it popular, but that is the origin of the motion. And for those of you rolling your eyes with your cursor hovering over the X button, let me move on to my point. If you have a superstitious character, you need to examine that character's religion in order to pick out points you can use to create superstitions. Assuming you aren't going to use pre-existing ones in the first place.
Then, of course, there's the last aspect of religion: the holidays. Which days demand reverence, which demand celebration? Even if you're choosing an existing religion, there might be days your character chooses to celebrate and ones he (or she) does not. Of course, that is true of every character, not just your mythological creatures.
Check back later this week for the conclusion of this mini-series: Language!