If one cannot win the White House, there is always the consolation prize of being the leader of the Presidential cabinet, as Secretary of State.
So we see a distinguished list of Presidential candidate losers who took on the most important and most publicized cabinet agency, the State Department. What follows is the list of these distinguished public servants and the national election that they lost.
Henry Clay (1824) was Secretary of State under John Quincy Adams.
Daniel Webster (1836) was Secretary of State under William Henry Harrison, John Tyler, and Millard Fillmore.
Lewis Cass (1848) was Secretary of State under James Buchanan.
James G. Blaine (1884) was Secretary of State under James Garfield, Chester Alan Arthur, and Benjamin Harrison.
William Jennings Bryan (1896, 1900, 1908) was Secretary of State under Woodrow Wilson.
Charles Evans Hughes (1916) was Secretary of State under Warren G. Harding and Calvin Coolidge.
John Kerry (2004) was Secretary of State under Barack Obama.
You could also add Hillary Clinton. She was also a Presidential candidate, even though she did not get the nomination.
Paul, the list in this posting are of actual nominees who lost the Presidency, and then became Secretary of State!