How can you protect a fragile object like bottle of champagne in your baggage against breaking?

Although I haven't brought champagne in checked luggage, I have brought wine on multiple occasions. (Typically bringing it home from places with nice wine.) I roll a nice soft Tshirt around it tightly, and if I have two bottles (which might clink against each other) then after each is rolled in a shirt I wrap the two of them together in another shirt or dress pants. Then the whole thing goes in the very middle of the suitcase with clothes and soft things all around. Never had a problem.

I usually go cheap and just wrap each bottle in half a dozen plastic shopping bags, one bag at a time. That way there's lots of air trapped in them, not unlike bubble wrap. Then I tuck those puffy, plastic bundles in the middle of my t-shirts or something.

We have packed a few bottles in tough cardboard tubes over the years, padding inside so they can't rattle and then we wrap the whole thing in a couple of garbage bags just in case the worst happens.

They've always arrived intact.

In a hardcase of some kind with foam inside. They are rather expensive but then again you can use them forever and for many different things.

I use it for computer and photo equipment. I put the case inside of my normal luggage, not as a separate item. But if your airline has nicer rules than most you might just add a few bucks and get away with shipping the hard case separately and freeing up some space in your other luggage :).

It is also worth checking at the airport transportation/goods department, they often have services of one kind or another for taking care of fragile goods. What exact services are available varies greatly between airports and regions. Anything from just a sticker to something like the mentioned hard case. This is usually not without a fee/service charge of some kind.

I did this a few years ago from the UK to New Zealand.

It's actually not as hard as it sounds. You can go the pro-way and use professional transportation foam, but if you have any bubble wrap lying around, that can be a handy alternative.

Myself, I wrapped all my shirts around the bottle. It becomes surprisingly snug and very unlikely to move, and has a lot of padding as a result. I quickly became confident in its security. And it also x-rays really easily like that.

San Francisco to Newark, two bottles of wine, wrapped in multiple shirts and packed in the middle of the luggage. I didn't worry too much about bagging them, because if the bottles break they are likely to cut the bags. Also, with 6 hours in flight the liquid is going to get out anyway if something goes wrong.

The best way is to use an inflatable protective packaging, like this: (source of image: a UK packaging company with whom I have no affiliation - googling for 'bottle postage inflatable' produces many alternatives).

As an additional useful tip, just in case your bottle (somehow) or you get a leak, wrap the whole lot in a tough old plastic bag (to stop shards going straight through) then in Saran wrap (US) / Cling film (UK). That way if the worst happens, you hopefully won't have a suitcase full of clothes soaked in wine. That saved me once with a bottle of red wine from which the cork inexplicably escaped (pressure differences I'm guessing).