We'll be going to Elba in early Sept. Is it necessary to reserve ahead if you are taking a car? We aren't sure exactly when we'll want to leave Piombino, so if there's a good chance of getting on a ferry without a reservation we'd prefer to do that.
There is no need to make reservations ahead of time. Early September still has a higher number of ferries running so you should have no problem showing up at the dock and purchasing a ticket at that point to make the crossing with your car.
The two main companies running ferries are Toremar and Moby in case you want to check how often the ferries run. Sometimes special offers are available online for reservations made on their site -- if the day before you want to make the crossing you have access to internet and have a better idea of when you'll arrive, you can still try to make the reservations ahead at that point. Otherwise just buy tickets there once you arrive at the port.