The two arrived late after their helicopter was forced to make an emergency landing minutes after taking off from central London.
Tributes have been paid to Princess Lilian, both in Scandinavia and in Swansea where she was born, after her death at the age of 97.
A church bell rescued from a devastating fire in Chile nearly 150 years ago and brought to Wales was be handed back in a service today.
The television series that documents Prince William's time with the Search and Rescue operations coincides with the news that the service is to be taken away from the RAF and privatised - a move that the prince is believed to have opposed.
ITV News' Royal Editor Tim Ewart reports:
Prince William is to feature in a BBC documentary about the Search and Rescue service, where he has served as a Sea King pilot.
You can watch a preview of the documentary below:
BBC One Wales have released a short preview video for Helicopter Rescue, the documentary featuring Prince William and the Search and Rescue team at the prince's base at RAF Valley on Anglesey.
The Duke of Cambridge is shown piloting a helicopter on a rescue mission to a slate quarry in Blaenau Ffestiniog.
One of his crew are winched from the ground after rescuing a boy who had fallen off an old railway bridge onto rocks.
"As captain you're trying to play out the entire rescue, the transit to the rescue and back again in your mind, and pick up any circumstances or problems you can foresee, and try and fix them on the ground before you get airborne," he says in the programme.
Among the 12 bases from where search and rescue operations are launched is RAF Valley on Anglesey, where the Duke of Cambridge is based.
Under the contracts due to be unveiled tomorrow, the total number of bases is expected to be cut from 12 to10 although it is not clear which bases will be closed.
Assurances have already been given that the Duke will be moved to another part of the military rather than being employed by the firm that is awarded the search and rescue contracts.
Carl Otto Werkelid, the Cultural Affairs Counsellor at the Swedish Embassy, told our presenter Andrea Byrne that Princess Lilian made a great contribution to Swedish society, and her style and beauty will live long in the memory.
These clips show Princess Lilian of Sweden and her husband Prince Bertil describing their sadness at not being able to have children together, but her happiness at becoming part of the extended royal family in Sweden.
– Cllr Dennis James, Lord Mayor of Swansea
Princess Lilian was one of Swansea’s most famous daughters.
Despite moving to London as a 16-year-old and then to Sweden, she remained proud of her Swansea links and this helped raise the city’s profile across Scandinavia and the rest of the world.
Her relationship with Prince Bertil was one of Sweden’s most enduring and best-known love stories.
This is a time both to mourn her passing and celebrate her 97-year life.
On behalf of the City and County of Swansea, I’d like to send my condolences to her family and friends.
Princess Lilian's death has been met with a great deal of sadness in Sweden, where she was a central member of the royal family.
Sweden's Foreign Minister Carl Bildt took to Twitter to say: "We feel truly sad for passing away of Princess Lilian. She was a most pleasant and truly wise person. She served her family and Sweden."
Swedish English-language news website The Local described her as "much loved", and "the grand old lady of the Swedish royal family".
Princess Lilian was "a credit to Swansea", her first cousin Barbara Davies, who was also born in the city, told ITV News.
"She had an exciting life. While living in Stockholm, she did have a degree of privacy."
"From my conversations with people in Sweden they were in high praise of her conduct."