The couple were greeted by cheers and a round of applause by school children from the region, who waved flags upon their arrival during Children’s Hospice Week.
The duchess was presented with a bouquet of flowers by 15-year-old Chloe Bowes, who has a neurological condition called bilateral perisylvian polymicrogyria.
Kate, who has been patron of EACH for 10 years, donned a floral face mask as she entered the hospice.
William joined her as they met three families who make use of the charity’s services, including 12-year-old James Hall, who has a genetic connective tissue disorder.
Kate placed her hand on James’s knee as she spoke with his mother, Claire, and his older brother Henry.
The duke and duchess were then greeted by Kirsty and Gary Carlin, whose four-year-old daughter Libby lay sleeping on the floor beside them.
After learning about her rare genetic condition, Libby’s parents offered to wake their daughter before the duke said: “Please don’t wake her.”
“We know what happens when you wake a sleeping child,” Kate added.
The couple then met the Carlson family, whose son William was lying on a bed in front of them.
The duke and duchess learned about the 11-year-old’s many complex medical conditions, including a brain malformation called lissencephaly.
The pair also took part in a small art session, where a canvas full of handprints was laid out in front of them.
Kate sat with an eight-year-old girl called Willow Bamber, who suffers from a severe neurological condition called Leigh’s disease.
The duchess invited the youngster to paint her hand, and as she tentatively started, Kate said: “Don’t be shy.”
Once her hand was completely covered in paint, she pressed her hand down on the canvas and was cheered as she lifted her hand up to reveal the handprint.
At the same time, William helped the children add to the canvas by sticking seaweed on it.
Before departing the hospice, William and Kate met the bereaved family of four-year-old Douglas Wright, who died from a rare cancer called neuroblastoma in February 2018.
As the couple sat down with the Wright family in the hospice’s sensory garden, they were told about the end-of-life care the youngster had received from the hospice.
“It brings back all the memories,” Douglas’s mother Jane said as she spoke about being back at the hospice.
Later on Thursday, the duke and duchess travelled to the first ever Cambridgeshire County Day at Newmarket Racecourse, and were greeted by cheers and applause from onlookers.
William and Kate both took part in a football game where they attempted to kick the ball at a target.
Kate told the crowd it would be difficult as she was “wearing wedges”.
After taking a shot, the duchess shook the hand of a boy who had been playing before her and said: “You did better than I did.”
The couple also sampled chocolate and a Jubilee beer before meeting members of the public while walking round a variety of stalls.
The event included stands from 120 exhibitors from Cambridgeshire businesses, charity, community and public sectors.
Kate spotted one woman holding a child and asked if she could hold her.
The baby’s mother, Marianne Provoost, who had travelled from the Netherlands to watch the races, said the duchess had asked to hold her child by saying: “I love babies.”
Her daughter, four-month-old Norah, was handed back to her, with Ms Provoost telling the duchess: “Enjoy your day and enjoy your children.”