So, for the sake of being absolutely correct, here is information on Andrew Johnson's return to the US Senate after his Presidency. While I had mentioned John Tyler's election to the Confederate Congress in my post, I admit I didn't know that Andrew Johnson was ever re-elected to the US Senate. Thanks for Coriolan for telling me about this.
Johnson died shortly after his 1875 election, but here is some information on the election and his short tenure (during this period):
In January 1875, Johnson won back his former Senate seat after a hotly contested struggle that forced the Tennessee legislature through 56 separate ballots. On March 5, 1875, Johnson took his Senate oath before the same body that only seven years earlier had failed by a single vote to remove him from the presidency. During the 19-day Senate special session, he delivered one major address—on political turmoil in Louisiana—and then returned to Tennessee, where he died four months later.
Another interesting tidbit I got from this site is that the Senate has considered letting former presidents sit in on Senate sessions and in 1963 granted them the right to address the Senate, though so far no one has done so:
In later years and without much enthusiasm, the Senate periodically considered proposals permitting former presidents to attend Senate sessions, either as at-large members or in some advisory capacity. Finally, in 1963 the Senate adopted Senator Claiborne Pell's amendment to Rule XIX allowing former presidents to address the Senate "upon formal written notice to the Presiding Officer." Although several ex-presidents have stopped by to say hello, none has yet chosen to make a formal address.