I use 1" Styrofoam sheets, cut to fit the box, with stand-offs of columns of stryro sheet in the corners, to support one or more "floors". On each floor, I place the models, and stick round, two ends points regular toothpicks, alongside the models where needed to prevent side by side movement. Each subsequent floor gets a "removal" finger hole in the center, to help lift out each level. Works to get to the local model meets, but won't work for shipping the models.
For shipping, I put each model into an individual ziploc type plastic back with just some of the air removed, and then place the bagged models into layers of styro peanuts or bubble wrap, in a cardboard box. That way, if small parts come adrift, you've got 'em captured!
Ed