I haven't shipped much, but I sure have received a lot of food over the years. Most arrive in Styrofoam containers which are kept cool using either dry ice or else some really good cold packs. These cold packs have more "heat capacity" than regular ice and, of course, don't turn into water and present a leak hazard.
Using these techniques, most items that started out frozen arrive frozen.
If I were to be the shipper instead of the customer, I'd use the same materials. In addition, I'd use the coldest freezer I have (-10 degrees F) and keep the item in that for at least 36 hours to make sure it would be frozen all the way. To give you some idea of how long something can stay frozen when it starts out at -10, I pulled out 2 pounds of chicken thighs seven hours ago and put them on the counter. They are still hard to the touch. If I had put them in an insulating container with cold packs or dry ice, I'm sure they'd be frozen for at least two days.
P.S. I just saw the post about Omaha steaks. I've had a few of these sent to me over the years and they are, by far, the worst meat I've ever had. I never throw anything out, but I tossed the last set.