Done it many times - and Yes. No tranquilisers.
I've always done it very matter of factly. They go in their carriers and the carriers are then secured inside the car in some way so that they can't move around - especially in the event of a road issue. (Best decide on that beforehand.)
Then I cover the carriers with a light coverlet to help their feeling secure but in such a way as to allow enough air and to give them a sight of me if they want.
They likely won't want to eat or drink during the journey, or to use a tray, but I'd take some food, water, bowls etc and a ready made litter tray just in case along with some kitchen towel and a few carrier bags in case of accidents. (Even if they don't use the tray during the journey and cross their legs it's always good to have a tray made up and to hand in the car - if nothing else, you can bang that into the room they're to go to at the other end as soon as you arrive and get them in there and safe while you unpack and potter.)
I know some posters have had good experiences with eg Feliway spraying and puppy training pads on the floor of cages so they may have suggestions on those.
It's not going to be their favourite moment but it should be quite doable. I've found that mine moan a bit for the first 10 minutes and then hunker down to grit it out with the occasional yowl just to let you know that they're still there. (I'd recommend a quick acknowledgement of any yowls but not much tea and sympathy.)
One important thing - don't ever let them out of their cages while the car is moving and unless the doors and windows are securely closed. The last thing you need is a loose cat in the car in the event of bad traffic conditions or a spooked cat at large on a motorway service area.
Have you got their accommodation at the other end sorted out in your mind?