There is a way to do it sediment free.
Make a cuvee that is around 11-12% (you can go higher, but the higher you go, the greater chances for failure).
When it is dry, fine/filter to get rid of all the yeast. Sterile filtration or pasteurization will make sure none are left.
Add the appropriate amount of fermentable sugar, and put it in Champagne bottles, and get some plastic champagne stoppers. These stoppers are hollow. Then take one gram of encapsulated yeast (Pro-Restart) - the uvaferm 43, DV10, or whatever version they have available and put it in the hollow stopper. Take a stainless steel faucet screen from a plumbing supply store and force it into the hollow opening trapping all the encapsulated yeast inside the hollow core of the stopper. Put the stopper in and wire it on. Turn the bottle so that the liquid is in contact with the stopper, and wait for the carbonation. Since the yeast are encapsulated in little balls, they don't leak out into the fluid (at least not much).
You can either leave the plastic stopper in, and just open it when you are ready to serve, or you can chill it down ice cold, and replace the stopper with a cork or crown cap if you prefer.
And there you have it - carbonation without sediment.