That's where a decanter comes in handy. I'll take an older wine out of my cellar a day or two before I plan to serve it, and stand it upright to let the sediment fall to the bottom of the bottle. Then ...

After a wine has been poured into a decanter ... Be prepared in advance with several decanters; how many depends on the size of the bottle being decanted and the size of the decanters you have ...