Only Republicans resign Senate seats to run for president (Barry Goldwater in 1964, Bob Dole in 1996).Goldwater did not resign his Senate seat. He chose not to run for re-election in 1964. Republican Paul Fannin won Goldwater's seat.
Goldwater returned to the Senate in 1968 when he defeated retiring Sen. Carl Hayden's chief aide, Ray Ellis, who ran to succeed Hayden.
For the Republican convention in 1968, Goldwater piloted his private jet into town, made a speech and flew back to Arizona to campaign. His "People Power" speech at the 1968 Republican Convention was the best speech of his entire career.
Thanks for the correction, but minor difference. The point I was making is that Goldwater's run for higher office did not include clinging to his present office-- unlike Joe Lieberman who ran for re-election and vice-president at the same time. If Goldwater had more than three months left on his term, I have no doubt he would have done the same thing Bob Dole did. It would have been rather pointless to have the governor appoint a replacement senator for three months when most of congress was out of session campaigning for re-election anyway.