I-Ching Cheng (26) failed to surface when she went for a swim at at Deadman's Point about 4pm on Friday.
Her body was found later that day.
Miss Cheng had been on a working holiday in New Zealand with her sister for the past year.
Today, Sergeant Simon Paget of Cromwell police said family members were en route from Taiwan, and Miss Cheng's sister was being supported by friends, police and Victim Support.
The matter was now in the hands of the coroner.