While William was on duty with his helicopter search-and-rescue squadron at a Royal Air Force station on the island of Anglesey in Wales, the duchess of Cambridge visited Naomi House in the English city of Winchester.
Naomi House is a hospice for children with life-limiting conditions who are not expected to live to adulthood.
Among the children Kate met was Sally Evans, an 8-year-old with spinal muscular atrophy, a genetic disease that attacks nerve cells nerve cells called motor neurons in the spinal cord.
Sally wished Kate a "happy anniversary and thanked her for choosing to come," Sally's mother, Sarah Evans, told People magazine.
Kate asked Sally what activities she likes at the center, Evans said, adding Kate was "so down-to-earth and friendly with the children."
The children gave Kate a felt-and-paper collage they made of the title character from the children's picture book "The Very Hungry Caterpillar" by Eric Carle.
"We thought we'd give you something not only to say thank you for being here but something to commemorate your anniversary," hospice Chairman Khalid Aziz said, adding he thought it might even be something Kate and William could "use in the nursery."
Kate, 31, is six months pregnant.
In Britain, traditional wedding gifts are made of cotton for the first anniversary and of paper for the second, the opposite of the U.S. tradition.
Kate released her first-ever video message Sunday in which she appealed for support for Children's Hospice Week.
William and Kate celebrated their anniversary with dinner in London Friday, after touring the "Harry Potter" and "Batman" film sets at a Warner Bros. studio outside London, Us Weekly reported.
William, 30, left for his air force duties Sunday and was to return after completing them Monday, the celebrity and entertainment magazine reported.