Vermilye was a Republican in politics and was involved as one of the commissioners of the New York Public School System. In 1863, W.R. and his brother William declined, along with President Abraham Lincoln, Robert B. Roosevelt, John J. Astor Jr. and Nathaniel Sands, to endorse John Adams Dix for mayor of New York City. In 1873, he wrote to President Ulysses S. Grant regarding the suspension of General Thomas B. Van Buren from his position as U.S. Commissioner to the Vienna Exhibition.