He was created Cardinal by His Holiness Pope John Paul II in the Consistory of November 26, 1994. As part of this service to the Church, he is also Pastor of the community of Aquila and Priscilla in Rome. He was received as Cardinal in the S.M.I. Cathedral of Havana on December 11, 1994.
Cardinal Ortega has been Vice President of the Latin American Episcopal Council (CELAM), President of the Conference of Catholic Bishops of Cuba in various periods, etc. For several years he has been a Counselor of the Pontifical Commission for Latin America, and belongs to the Congregations for the Clergy and for Health Pastoral Care.
He has been awarded with Honoris Causa doctorates from the Universities of St Thomas and Barry in Miami Florida, Providence, Rhode Island, University of San Francisco, the annual prize of the Bonino Pulejo de Messina Foundation, the Gaudium et Spes, the Knights of Columbus, 
among other international recognitions like the Doctorate Honoris Causa of the University of Creighton, in the United States and the Medal of the Catholic University of Eichstätt, in Germany.
Given the uniqueness of Cuba in the global context, it has had to hold meetings with dignitaries from various countries, including Presidents, representatives of various Royal Houses, ministers, representatives of the Diplomatic Corps accredited in Cuba, etc., who appeal to him interested in Cuban affairs.