As a homebrewer and past beer trader I was often faced with shipping the bottles to their destination for judging or trading. First and foremost DO NOT try to ship these with USPS, that will not fly. The AHA at one time was trying to get an exemption for homebrew competitions, but to my knowledge that has not happened so it is verboten to ship alcohol via USPS. So your choices are UPS and FedEx and I believe both have internal policies against shipping alcohol with a few exceptions. Since you are not trying to sell the hooch, just get it evaluated by judges or traded to another person I’d suggest you adopt a don’t ask don’t tell policy. If you go to a shipment site and they ask what is in the package it will most likely be rejected if you are truthful, and you should be truthful. The better option is to package yourself and then purchase the shipping online and simply drop off with no questions asked. Now keep in mind if a bottle breaks and the package leaks it will most likely be discarded and you will lose all the contents so package well.
Let’s take a minute and discuss how to package. I find it best to avoid leaks so first carefully line the box with a large garbage bag, this will be your last line of defense against leaks. Be sure when packing the box to not tear the bag. Now take each bottle and secure it in a ziplock. Often this will require putting the bottle in at an angle. Next wrap it in large bubble wrap. I find the large bubble does much better than the small. Whenever I receive a package with bubble wrap I save it for shipping. Tape up each bottle so no glass can contact other glass. Before placing the bottles into the box think about how glass can break. It could break by the glass being near the edge of the box and taking a direct hit or by two bottles slamming together. To avoid this cover the inside of the garbage bag with a layer of bubble wrap on the bottom and sides. Now start putting in your bottles and separate with more bubble wrap or wadded newspaper. Often Amazon packing materials can be reused for filling space. Once everything is in the box cram as much lightweight material in the box so it will barely allow you to close the bag and box. Now shake the box and if you hear movement fill in any gaps. If you do not feel comfortable slamming the box to concrete from a height of six feet you have not packaged well enough. Once you feel comfortable doing that you have packaged the box correctly.
You can save some of that effort by obtaining shipping boxes made for wine or beer. They are expensive to purchase and typically do not hold very many bottles. Smaller bottles will still take additional packaging materials to fill any gaps. If you are shipping liquor the bottles, when glass, are typically thicker than beer bottles and can withstand more force. I received a gift from a friend which was somewhat poorly packaged, but made it just fine. It was a bit of a miracle, but the bottles made it despite their packaging methods. So the moral of the story is purchase shipping online and drop off a well packaged box and all should work out well most of the time.