"I've known him since he was little and we just sniggered at each other," she told reporters after Wednesday's investiture ceremony in London.
The Oscar- and Bafta-winning star said it was "a very lovely feeling" to become a dame for services to drama.
The event also saw another actress, Sarah Gordy, become the first woman with Down's syndrome to be made an MBE.
Gordy, who has appeared in Call the Midwife and Upstairs Downstairs, said it was "just fantastic" to return to the palace, having previously visited as a celebrity ambassador for the charity Mencap.
"I've worked really hard in what I believe in," said Gordy, who was recognised for her services to the arts and people with disabilities.
"I'd like to inspire others and empower others to believe in themselves, especially people with Down's syndrome."
Meanwhile, Dame Emma highlighted her own activism after the ceremony, describing herself as "a card-carrying feminist" and "human rights advocate".
"I'm very outspoken politically," said the 59-year-old, adding that she hoped to use her damehood to bring attention to so-called "holiday hunger", which sees up to three million UK children go hungry during the school holidays.
Dame Emma, who arrived at the Palace in white trainers and an emerald Stella McCartney suit, was joined by her husband Greg Wise and their children Tindy and Gaia.
The actress, whose recent credits include Johnny English Strikes Again, is currently filming Russell T Davies' new TV drama Years and Years, in which she plays an ambitious politician.