It comes and goes for me. I've found the best thing is to have something good to fix my mind on as I go to sleep. I have a book that gives a selection of Bible verses for each morning & evening and I often pick one of those verses to think about when I put the light out. I know this might not be acceptable for everyone depending on your beliefs, but you could try the same idea using a poem, positive saying or a happy memory. Or list all the blessings in your life. Every time a worry pops up, remind yourself you are not dealing with that now, you are thinking about good things. I've also found that if I go to sleep dwelling on good things, I am less likely to panic when I wake in the night. And if I do, I just pick up where I left off.
BTW, this assumes the anxieties are not about 'realistic' things or are excessive. If you're worried about real stuff, then make time earlier in the day to think through them and work out what, if anything you can do about them.