Preserving leftover, partially drunk Champagne is done exactly in the opposite way one preserves wine.  An unopened bottle of Champagne contains a lot of pressure, as one can see when opening a bottle of Champagne.  To preserve the “bubbly”, the essential effervescence of Champagne, the bottle needs to be repressurized.  By adding air and pressurizing a bottle of Champagne will keep a bottle for several days.

Check out the Champagne Stopper by MITBA.