The rescue of a married couple in their 70s who had been lost in the woods for more than a week is being hailed as a miracle by authorities in Northern California, who had given up hope of finding them alive.

Carol Kiparsky, 77, and her husband, Ian Irwin, 72, were located in a densely forested area near a bay about 30 miles north of San Francisco on Saturday, two days after the Marin County Sheriff’s Office had switched from search mode into a recovery mission.

The Palo Alto couple had been missing since leaving their vacation cottage and getting lost on a Valentine’s Day hike. They were airlifted by helicopter to get treatment for what Sheriff’s Sgt. Brenton Schneider described as “slight hypothermia’’ but were otherwise doing well.

Search efforts that involved hundreds of people, boats, a plane, drones and trained dogs around the bayside town of Inverness failed to yield results until the couple was heard calling for help Saturday morning, a few miles from their vacation lodging.

Schneider said they survived by drinking water from a puddle and may have fallen near the drainage area where they were found. At the time, Kiparsky was missing a shoe and Irwin did not have a jacket.

“This is a miracle,’’ said Schneider, who added, “They thought this was the end for them.’’

Questions remain: Why did it take months to issue an Amber Alert for missing Tennessee toddler Evelyn Boswell?

At one point, Kiparsky set out on her own to seek help, tying pieces of her scarf to branches to point the way back to her husband.

They had gone on the hike without food or water and left their cell phones and wallets behind. Those were reported missing by housekeepers after the couple failed to check out of their cottage as scheduled on Feb. 15. Their car was parked outside.

After days of exhaustive searching, the sheriff’s office acknowledged the likelihood it wouldn’t succeed with a Thursday news release that said, “We believe that our extensive search efforts with every resource that has been available to us would have located Carol and Ian if they were responsive or in an area accessible by foot on land.”

On Saturday, they were happy to be wrong.

The rescue of Kiparsky, the author of several books on language, and Irwin, a leading Parkinson’s researcher, capped a hectic but ultimately rewarding week for search teams in Marin County. On Tuesday, they found another missing man in his 70s, Robert Bennett, alive with the help of two dogs a day after he had a stroke and fell during a hike.

Contributing: The Associated Press

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