Another thing I thought of was that demystifying things that scare your kids, if possible, is a very good way to help them deal with fear.
When my son first started getting afraid of monsters, I tried saying, “There aren’t any monsters,” or “They’re more afraid of you than you are of them,” both things my mom used to say without any luck getting me to believe her. So, I decided that if that didn’t work, maybe it would help to get him to help me drive the monsters out. So, one night when he was worried about monsters, I asked, “Hmmm…Do you want me to tell them to go away for you? Will you help me?” He said yes, we yelled at the monsters to go away and, since then, the monsters haven’t come back.
I did something similar with thunderstorms. He was terrified that the thunder was going to come into the house and eat him, so one evening during a storm, I carried him out to the porch (I wouldn’t have bothered if he were trying to get away; he was more uneasy than anything else), and we danced around while the thunder boomed around us. Now every time there’s a storm, he wants to do the thunder dance.
I think it’s important to acknowledge your kids’ fears and let them know that you think they’re valid. Not necessarily that they should be afraid, but instead treat them as real things that can be handled.