Ms Tate, a leading constitutional and commercial lawyer who is the first female solicitor-general of Victoria, in Australia, graduated with a BA (hons) in philosophy at Otago University in 1979.
She later also gained a BPhil at Oxford University.
She made her comments to about 480 graduates in commerce, tourism and law at an Otago University graduation ceremony at the Dunedin Town Hall on Saturday.
The confidence of graduates in their future could be "sorely tested" in the current global economic climate, she warned.
Those supporters who had made sacrifices for the new graduates all hoped and believed the degrees would have a benefit.
"These are your parents, your partners and your friends, many of whom are here today, who gave their time or their money, or met the demands for super-human tolerance that you placed on them.
"You and they must not lose confidence that those practical benefits will eventually come."
Ms Tate recalled a friend of hers who had, a year after graduation from Oxford University, received enough rejection slips to paper the walls of his flat.
"This was a flat that was as cold as any in Castle Street, a flat where the landlady explained, in a chirpy and co-operative manner, that she didn't bother to supply a fridge because the rooms were so cold that no fridge was needed."
The Oxford friend had never lost confidence, plucking rejected applications from one envelope and sending them off in another.
He was now a professor, she added.
The skills and knowledge with which Otago University had equipped graduates amounted to more than the technical expertise of a particular profession.
Students had also gained "the critical capacity to adapt" - including from one discipline to another.
An Otago University degree rendered their future "sure-footed", she said.
"The debt you owe to Otago University-as do I- is that it is an institution which sets out to cultivate and nourish a lifelong love of learning.
"It is that continuous desire to learn which will enable your future careers to have sparkle and, more importantly, will enable you to continue to grow as people."
Ms Tate also has an honours degree in law from Monash University, Australia, and holds the title senior counsel (SC), the modern Victorian equivalent of the former Queen's counsel (QC).
