Born in Clymer, New York, Amidon received an Artium Baccalaureus degree from Hamilton College in 1882 and read law to enter the bar in 1886.

[2] Amidon received a recess appointment from President Grover Cleveland on August 31, 1896, to a seat on the United States District Court for the District of North Dakota vacated by Judge Alfred Delavan Thomas.

He was confirmed by the United States Senate on February 18, 1897, and received his commission the same day.

His service terminated on December 26, 1937, due to his death in Tucson, Arizona.

He was the last federal judge in active service to have been appointed by President Cleveland, and the longest-serving.