The Robert G. Storey International Award for Leadership is named after Dean Robert G. Storey, the founder and first President of CAIL. Among his many roles, Dean Storey was President of the Center, Dean of the Southern Methodist University Law School, and President of both the American Bar Association, and the Inter-American Bar Association. In recognition of his dedication to peace, justice, and the rule of law in the international community, CAIL has established the Robert G. Storey International Award for Leadership.

From 1990 to 2017, the Storey Award has been presented to former participants in the Academy of American and International Law who have exhibited the qualities of leadership and integrity embodied in Dean Storey. 

The Award has previously been presented to: 

• 2017 - Mohamed Shafie Ameermia, then Commissioner of the South African Human Rights Commission
• 2015 - Enzo Moavero Milanesi, former Italian Minister, European Affairs and Past Director General, European Policy Advisers Bureau for the European Commission
• 2013 - Lilia de Lima, then Director General of the Philippine Economic Zone Authority and member of the Philippine Cabinet
• 2010 - Bernard Hanotiau, a world-renowned arbitrator and a founding member of the Belgium law firm of Hanotiau and van den Berg;
• 2008 - Jose Luis de Salles Freire, founding partner, Tozzini Freire Advogados of Brazil;
• 2004 - Beatriz Merino, former Prime Minister of Peru; 
• 2003 - Santi Thakral, then immediate past President of the Supreme Court of Thailand; 
• 2001 - Kunio Hamada, then Justice of the Supreme Court of Japan and Founding President of the Inter-Pacific Bar Association;
• 1998 - Didier Opertti, former Minister of Foreign Affairs of Uruguay (and later the President of the U.N. General Assembly); 
• 1997 - Antonio Cassese, then President pf the United Nations International Criminal Tribunal for the Former Yugoslavia; 
• 1996 - Raul I. Goco, then Solicitor General of the Philippines and former President of LAWASIA; 
• 1995 - Rene Blattmann, then Minister of Justice of Bolivia; 
• 1993 - Sergio Abreu, then Minister of Foreign Affairs of Uruguay; 
• 1992 - Antonio Brancaccio, then Chief Justice of Italy's Supreme Court of Cassation; 
• 1991 - Mochtar Kusuma-Atmadja, former Foreign Minister and former Minister of Justice of Indonesia; and
• 1990 - Marcelo B. Fernan, then Chief Justice of the Philippines (and later President of the Philippine Senate).