In order to acquire the super sledge, simply speak to Fawkes when he is taking you to the G.E.C.K. and ask him to trade. It will usually be in his inventory as an equipped item unless he has grabbed a better weapon on the way or was relieved of it by enemy attacks. He may occasionally have more than one. If taken from him, he will equip a sledgehammer which cannot be traded.
If you miss this opportunity, Fawkes may still have the weapon when he is seen outside Raven Rock, and it can be acquired through the same means. If not, you can go back to Vault 87 when you have Fawkes as a follower and he will equip the weapon. You must be in the experimental section of Vault 87 where Fawkes was originally found for him to equip it. If you have low Karma, he will not become your follower, so you will either have to kill him, pickpocket the weapon, or shoot it out of his hands to take it.
It is possible to acquire his super sledge if he has returned to the Museum of History. With a high Sneak skill you can pickpocket it off him.
With Broken Steel installed, Fawkes may have the super sledge following the events of Take it Back!, assuming he is not your follower at the time.
Playstation 3Xbox 360 Using the Medical Wing Maintenance terminal and releasing Iso Room 5 after Fawkes has been freed will add a copy of the unique weapon to his inventory (regardless of the method used to free him). Each time you release the room, another copy will be added, allowing for infinite copies (extremely quickly too, since you do not need to leave the terminal interface for them to be added). [verified]
Playstation 3Xbox 360 You can add a number of super sledges that exceeds Fawkes' carry weight via the aforementioned bug. Doing so will not slow him down in any way. However, removing them from his inventory and trying to give them back to him will yield the message "Fawkes can't carry any more." [verified]