For the small models you can see what I did, for the big models (1/72 B-36, B-52 and some other I had to do it differently. The first problem was finding a box big enough, the moving companies have boxes which you can buy from them but they're a set size (designed to load into trucks, vans or trailers exactly)
Finding a box for the B-36 I had built was the most difficult (the biggest I had built up to the move) -- at the beginning. I needed something about 34" square. You can get boxes made to suit however -- but it is very expensive so don't go that route. There are places though that have plenty of spare boxes, which they just throw away. There's Leon's, The Brick, Sears ----- see where I'm going --- Not long before we decided to move we had bought a new washing machine, it came in a very big box, placing the B-36 on top of the machine I found that it was just a little smaller that the machine top, so I called Leon's to see if the had a box I could buy. This was when I found out they have hundreds of boxes of all sizes which come in very handy for packing things in, flat screen TV boxes for instance make very good picture frame packing boxes. Anyway I went to Leon's and saw the manager of the shipping section and he 'gave' me a whole load of boxes.
Next was figuring out how to store the big models in the box, sometime ago, me and my Dad used to make flying gliders and they were stored in frames to keep them secure, I decided to do the same only using the styrofoam boards. I carefully measured each model and then made a bottom frame and a top frame out of these boards. Then I got some cheap 1/4" plywood which was then cut to fit as snuggly as possible in the big washing machine box. I glued the bottom cradle frame to a plywood board after cutting out half circles or half chord shapes so the fuselage and wings would sit in it, then doing the same to the top cradle frame. I used long construction nails to hold the top cradle to the bottom cradle. So I didn't waste space in my box, I cut strategically place openings in each plywood board so tall bits (like fins etc) could poke through. In the pics below you can see the result