In the current climate of shortages of high-quality engineering graduates, exacerbated by reduced high school enrollments in physics and mathematics, engineering faculties are becoming increasingly aware of the importance of K-12 outreach programs. Such programs can result in students being better prepared for and better informed about engineering careers, with a consequent increase in the number of engineering undergraduates. Almost all outreach programs described in the literature are school-based; by contrast, this paper describes a university-based program. The program was born out of a desire for a university department and a neighboring high school to forge closer links and a need for the high school to provide its students with certain laboratory experiences that would best be realized with the use of specialist equipment. The outreach program provides both formal laboratory experiences and informal presentations by graduate students of their research interests. Follow-up surveys showed that the high school students found the experiences both instructive and motivating, and their knowledge of and interest in electrical engineering increased significantly as a result. All final-year physics students from the high school took part in the 2007 outreach program, and 42% of these students subsequently enrolled in the Bachelor of Engineering degree at the university in 2008. (Contains 2 tables, 1 figure, and 2 footnotes.)