The one port for which Board of Special Inquiry records survive is Philadelphia. There are 18 National Archives microfilm rolls covering the years 1893 - 1909.
The records are viewable on Ancestry.com
http://search.ancestry.com/search/db.aspx?dbid=2892If you read a few of the records you can get an idea of how the hearings were conducted and the nature of the questioning. You will see why most detainees were ultimately admitted.