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 provided that his entire estate, excluding three annuities, be donated to the University of Western Australia to fund scholarships in applied science. These funds began supporting the Robert Gledden and Maud Gledden travel fellowships at £750 per year after ten years posthumously. Furthermore, there are Gledden scholarships for engineers or surveyors to study elsewhere in Australia, and additional Gledden scholarships for students in engineering, surveying, or applied sciences.