The pair, Kate wearing a grey coat, black gloves and black stiletto heels and Mary a white coat with a black dress and black stilettos, waved to onlookers at Amalienborg – the home of the royal family in Denmark .
Kate and Mary were set to visit a shelter helping women and children who have been exposed to domestic violence.
Earlier, Kate enjoyed a taste of the great outdoors as she split firewood with children.
She visited Stenurton Forest School on the outskirts of Copenhagen, where pupils are taught outside as part of efforts to boost their wellbeing and tried her hand at splitting logs.
She beamed as she swung a hammer at a block three times before it broke in half.
Teaching assistant Carla Bro said: “She was very good… and had good focus.
“She asked how we deal with risky play and how we keep things safe. We have safety rules and we teach the children they should not be afraid of tasks but treat them with respect.”
Kate, who looked relaxed in a grey jumper, a £209 green Seeland wax jacket and a pair of black jeans, is on the final day of a whistlestop trip to learn how Denmark has become a world leader in early childhood development.
After hearing how children travel from city centres to play outdoors instead of in classrooms, she took part in a “wing friend” exercise grabbing a child’s hand and running through the woodland — designed to teach the importance of working together. To cap the hour-long visit, she then joined the children in a mindfulness session.
Kate launched her Royal Foundation Centre for Early Childhood last June, which aims to increase awareness of the “extraordinary impact” of youngsters’ early years to “transform society”.
Later she was having an audience with Queen Margrethe II and Crown Princess Mary at Christian IX’s Palace.
Yesterday, Kate got into the spirit of learning about children’s play by trying the slide at the Lego Foundation. She confessed her children were jealous she was visiting Lego without them. The duchess is due back in Britain tonight.