One power unique to the Senate is that the it is the only body that tries the president in case of impeachment. The House of Representatives impeaches the president, but the Senate conducts his trial.
According to Article I, Section 3, Clause 6 of the United States Constitution, "The Senate shall have the sole Power to try all Impeachments . . . And no Person shall be convicted without the Concurrence of two thirds of the Members present." The Chief Justice of the Supreme Court presides over such a trial. According to the United States Senate, as of May 2014, only two Presidents have been impeached and faced trial by the Senate: Andrew Johnson and Bill Clinton.