The Chief Justice of the Supreme Court is supposed to swear in president-elect of the United States. If there is no sitting Chief Justice, another member of the court would swear the president and vice-president in.
However, what if the entire court does not have any sitting members. Who swears in the president then? Ideally, the Senate would have to approve a new presidential nominee. But what if the entire court is killed in a tragic accident on their way to the new president's inauguration on the 20th of January?