Both actresses, who were driving separate cars when they were arrested Dec. 1 within 15 minutes of each other, were represented by their attorneys.
Watros' attorney Lanson Kupau was granted a continuance of the arraignment to Jan. 12, when she will plead guilty and take "full responsibility."
"She made a mistake. She's very remorseful and she wants to take responsibility for her actions," Kupau said in an interview.
Watros, 37, who plays Libby on the ABC's hit castaway drama, was in California spending time with her family.
"She realizes, understands and appreciates the seriousness of the charges," Kupau said. "We will cooperate and she will take responsibility."
Police said both women failed field sobriety tests and were released on $500 bail each. The actresses were arrested after their vehicles were spotted weaving in Kailua.
Trial was set for March 30 for Rodriguez, who plays police officer Ana Lucia on "Lost," which is filmed in Hawaii.
Her attorney Steve Barta had no comment following the hearing.
Last week, prosecutors in California filed a motion in Los Angeles Superior Court to revoke Rodriguez's probation because of her drunk driving arrest in Hawaii.
In June 2004, Rodriguez pleaded no contest in Los Angeles to three traffic violations: hit and run, drunken driving and driving with a suspended license. She completed a three-month alcohol program and is now serving a three-year probation term.
Prosecutors in Los Angeles on Jan. 24 will ask the court that a probation violation hearing be scheduled.
Rodriguez has been pulled over by Honolulu police multiple times since joining the cast this season. She was cited for driving 83 mph in a 55 mph zone on Oahu on Nov. 1 and was fined $357.
The 27-year-old actress also paid a $300 fine for an earlier traffic offense on the island. She was cited for driving 90 mph in a 35 mph zone on Oct. 20.
Previously, Rodriguez was fined $197 for going 80 mph in a 50 mph zone on Aug. 24.
City Deputy Prosecutor Sean Sanada said Rodriguez and Watros are not getting any special privileges because of their celebrity status.
"We're treating them just as we would treat any other citizen or any member of the public," he said.