The Florida State University named its tennis center after Speicher, an avid player. The $1.2 million Scott Speicher Tennis Complex was completed in 2003. In 2018, FSU President John Thrasher joined members of Speicher’s family to unveil a new memorial honoring Speicher. The memorial, located at the entrance of the tennis facility named after him in 1993, features a bronze Navy pilot’s helmet and oxygen mask and will eventually include a bronze Navy G-1 flight jacket and naval officer's khaki garrison cap similar to what Speicher would have worn.