President Warren Harding died in San Francisco on August 2, 1923. His vice president, Calvin Coolidge was, at that time, visiting his family in Vermont.
Harding had been ill for several days, in the midst of a west-coast trip, but his condition was not at first thought to be life-threatening. I presume that's why Coolidge felt free to vacation at what didn't seem to be a time of crisis.
As I wrote here, under those circumstances, one of the first questions is: who will administer the oath of office? In almost all cases, that has been a federal judge. However, there is a school of thought that says that anyone who regularly administers oaths can handle the task at the presidential level.
Coolidge's father, John Coolidge, was a notary public. John Coolidge had awakened his son, when a telegram arrived at the farmhouse that lacked electrical and telephone connections, bringing news of Harding's death. The decision was made that the father should swear the son into office.
The room in which the new president took the oath, is preserved at the Coolidge historic site in Vermont, and is rather grandly called "The Oath of Office Room". I visited the site five years ago. It's worthwhile for any presidential history buff to include it on a tour of New England.
When Coolidge returned to Washington, he repeated the oath before a federal judge, to forestall any questions regarding the validity of an oath administered by a state official.