Yesterday two Burmese migrants were told they face the death penalty for the brutal murder of the 24-year-old on a beach in Thailand last September.
A statement from the police said: “Throughout this exceptionally difficult period the States of Jersey Police have provided support to the family of David Miller by way of local Family Liaison Officers.
“The courage shown by David’s family throughout this exceptionally stressful period has been humbling to all those involved. Our thoughts go out to them at this time.
Bar workers Zaw Lin and Wai Phyo, also known as Win Zaw Htun, initially confessed to the murders but later retracted their statements, claiming they had been tortured by police.
The long-awaited verdicts in their trial were delivered at a court on the island of Koh Samui on Christmas Eve as both men were found guilty of murder and rape and issued with the death penalty.
Miss Witheridge, from Hemsby in Norfolk, had been raped before she was killed, while Mr Miller had been hit over the head before drowning in the sea.
Jersey Police said: “Our officers have received invaluable guidance from the National Crime Agency and the Foreign and Commonwealth Office and we thank them for their assistance.”