How can I keep leftover Champagne or Prosecco bubbly? Do Champagne stoppers work?

Hello there! I'm Dr. Vinifera, but you can call me Vinny. Ask me your toughest wine questions, from the fine points of etiquette to the science of winemaking. And don't worry, I'm no wine snob—you can also ask me those "dumb questions" you're too embarrased to ask your wine geek friends! I hope you find my answers educational, empowering and even amusing. And don't forget to check out my most asked questions and my full archives for all my Q&A classics.
Dear Dr. Vinny,
Is there any way to keep leftover Champagne or Prosecco bubbly? Do Champagne stoppers work?
—Jerry, South Carolina
Dear Jerry,
I have a couple of Champagne stoppers on hand with a rubber inner ring and two hinges that latch on to the bottle. They work quite well—I can get an extra day or two of life out of a bottle of bubbly without losing much carbonation.
Unfortunately, they don’t work on every bottle shape, depending on the size and placement of the lip near the bottle opening. Stoppers generally cost about $5 to $10, though the cheaper ones can have sharp metal edges, and I’ve cut myself before.
I should warn you that while these stoppers can work, they cannot keep a bottle from leaking if you store it on its side. You’ll need to make some room in your refrigerator so the bottle is stored upright.
—Dr. Vinny