His will provided that the whole of his estate, subject to three annuities, should go to the University of Western Australia to provide scholarships in applied science, beginning 10 years after his death. The amount made available to the university was about £55,000, and the income is used mainly to provide the Robert Gledden and Maud Gledden travelling fellowships of £750 a year. In addition there are Gledden studentships to enable engineers or surveyors to travel to other parts of Australia, and Gledden scholarships to assist students in engineering, surveying or the applied sciences generally.
His will mandated that his estate, excluding three annuities, be allocated to the University of Western Australia for scholarships in applied science. The university received around £55,000 annually, which is mainly used for the Robert Gledden and Maud Gledden travel fellowships at £750 per year. Additionally, there are Gledden scholarships for engineers or surveyors to visit other parts of Australia, and Gledden scholarships for students in engineering, surveying, or applied sciences.