Camilla, Duchess of Cornwall, joked there would be "no talk of rivalry" as she presented an honourary degree to her sister-in-law, Princess Anne, in her capacity as chancellor.
Known as the Duchess of Rothesay in Scotland, Camilla awarded the Princess Royal an honourary degree of Doctor of Laws for her charity work and contribution to sport.
The duchess said she was not sure if there a "collective noun for chancellors" before telling guests: "Ladies and gentlemen, we shall have no talk of rivalry today.
"But I might just casually observe that, while we are to celebrate our 525th birthday next month, the University of Edinburgh is comparatively youthful – a mere 437-years-old."
Anne is chancellor of another Scottish university - the University of Edinburgh.
And Camilla imparted some cryptic advice on students at the university, when she quoted from Scottish writer, Nan Shepherd.
"I will finish with a quotation from Nan Shepherd, famously she wrote in her book, The Quarry Wood, 'It's a grand thing to get leave to live," Camilla said.
"This is a university with an extraordinary heritage of giving its students and its graduates leave to live.
"You will no doubt continue to do so over the next 525 years."
The Princess Royal received a Doctor of Laws for a lifetime of charity work in a ceremony at the university’s Elphinstone Hall on Tuesday.
Anne is involved with 300 charities in the UK and overseas, including serving as patron of Save the Children.
She said it was a "real honour" to be recognised by the university.
Anne undertook her first public engagement at the age of 18 and since then has had one of the busiest working schedules of any member of the royal family.
In her speech, the Princess Royal paid tribute to fellow honorary degree recipient Professor Janet Darbyshire, recognised for her work in clinical sciences, who she said she had met through Save the Children.
Previously director of the Medical Research Council clinical trials unit, Ms Darbyshire’s study of diseases such as HIV and tuberculosis has led to improvements in prevention and treatment across the world.
The Denis Law Legacy Trust, which supports children and young people through its Streetsport project, received a special award for outstanding service to the community.
The Princess Royal said she met the ex-footballer when they shared front row seats at the BBC’s Sports Personality of the Year ceremony in Aberdeen in December.
“There’s no doubting the fondness for him here in Aberdeen,” she told guests.
The University of Aberdeen was founded in February 1495 – which chancellor Camilla said “by happy coincidence” was the year of the earliest written record of the distillation of Scotch whisky.
She said: “Next month, your proud chancellor will make sure she toasts your birthday with a wee dram.”
The duchess later attended the official opening of Banchory Sports Village on Royal Deeside, where the royals traditionally spend a summer break at Balmoral Castle.