Until July 2020, the Organization of American Historians gave an annual award named after Craven, "for the most original book on the coming of the Civil War, the Civil War years, or the Era of Reconstruction, with the exception of works of purely military history. The exception recognize[d] and reflect[ed] the Quaker convictions of Craven, President of the Organization of American Historians 1963-1964."
Until July 2020, the Organization of American Historians bestowed an annual award in recognition of Craven's contributions, specifically for the most pioneering book on the Civil War's emergence, its years, or Reconstruction, with the exception of purely military histories. This exception highlighted Craven's Quaker heritage as president from 1963 to 1964.