Just-shipped Madeiras should also rest—standing up, of course. For how long depends less on the wine’s age than when it was bottled.
As casks of very old Madeira gradually vanish from the island, fewer old Madeiras are being bottled. Those that are bottled increasingly carry a bottling date on the back label. If your Madeira’s label shows that it was bottled within the past four or five years, the wine may need only a few days to recover from shipping. But an old Madeira that’s been in bottle for decades may need months to regain its clarity and balance after shipping.
Madeiras love oxygen, and so early decanting is often important - not just to remove sediment, but for breathing. Because of the decades they spend in the oxygen-rich environment of a barrel, Madeiras respond to air unlike other wines. They tend to shut down when bottled, and the longer they're in bottle, the more air they need to open up again.
An old Madeira customer once suggested this useful rule of thumb: for each decade the wine has been in bottle, give it a day in the decanter. A Madeira that's been in bottle for just two or three years will show superbly with just a few hours breathing, but a wine bottled in the 1970s would ideally be decanted three or four days before serving. And don't worry about giving an old Madeira too much air; once open, it will drink beautifully for months, if not years. Just put a cork in the bottle, and revisit it again and again.
While almost all wines should be stored long-term on their sides, Madeira is different. It should be stored standing up. Madeiras tend to destroy their corks, and far too many great old Madeiras lying in bins have lost their contents when their corks gave out.