The parents of six-day-old Eliza-Mae, who is thought to have been killed by the family dog, said they will "cherish the little time we were able to share with her".
Eliza-Mae Mullane was airlifted to the University of Wales Hospital in Cardiff yesterday after what is thought to have been an attack by the family's Alaskan malamute dog.
"Even though she was an important part of our family for such a short period of time, Eliza-Mae will always be in our hearts and thoughts and we will cherish the little time we were able to share with her," Sharon John and Patrick Mullane said in a statement.
"She was a dearly loved daughter, sister, granddaughter and niece. She brought joy into our family, and losing her like this has cast the most horrible shadow over all of us.
"There are no words we can use to describe what we feel at the moment, and we don't think there ever will be."
More top news
Hot and humid throughout the Bank Holiday Weekend.
The airline has cancelled all flights from Heathrow and Gatwick before 6pm on Saturday.
The Hollywood couple, who have been married for 17 years, said they still have "tremendous love and respect for each other".