Garrett had an early intensive interest in science, especially in history and archeology, and became an early collector and important donor. He helped to organize and finance an archaeological expedition to Syria, led by Dr. John M. T. Finney. From 1932 to 1939, he was involved with the Committee for the Excavation of Antioch and Its Vicinity both helping to fund the excavations and working on them. Garrett's hobby was collecting medieval and Renaissance manuscripts. Garrett amassed a collection of historical volumes of Western and non-Western manuscripts, fragments, and scrolls, originating from Europe, the Near East, Africa, Asia and Mesoamerica, ca. 1340 B.C. – A.D. 1900s. He inherited his collecting interest from his father, Thomas Harrison Garrett. After his father's sudden death in 1888, Robert spent the following two and a half years traveling extensively with his mother and two brothers, Horatio and John, in Europe and the Near East. During his travels Garrett developed a particular interest in manuscripts and began collecting. He used the text Universal Paleography: or, Facsimiles of Writing of All Nations and Periods by J. B. Silvester (by Sir Frederic Madden, London, 1949–50) as his guide for collecting primary examples of every known type of script.