Walking around the campus of Westminster College with Tim Riley is like going back in time.

He can point out the exact spot where Winston Churchill got out of his car when he visited in 1946. In the college’s gymnasium, he points out the metal pole still strung to the building’s rafters, where a special backdrop was hung for the occasion. Standing outside the old university president’s house he recounts, as the story goes, how Churchill commented during their lunch: “Madam, I believe the pig has reached its highest state of evolution in the form of this ham.”

Mr. Riley is the director and chief curator of America’s National Churchill Museum at Westminster College in Fulton, Mo. As such, he leads the efforts to preserve the legacy of Churchill’s visit to the town, about 90 minutes west of St. Louis.

“The 50-minute speech that Churchill gave that day on March 5 changed the course of 20th-century history,” Mr. Riley said almost as nonchalantly as he recalled Churchill’s praise of Callaway County ham. It was here on March 5, 1946, that Churchill gave a speech titled “The Sinews of Peace” where he warned of the Cold War’s earliest chill, coining the term “the Iron Curtain.”