After a two-week sojourn in the Sacramento-San Joaquin River Delta, two lost humpback whales were closing in on a return to their ocean home.

The mother humpback and her calf made considerable progress Tuesday and were last seen less than 10 miles from the Golden Gate after they passed under a busy bridge and entered San Francisco Bay.

"They're heading very much in the right direction," said Rod McInnis, a spokesman for the National Oceanic and Atmospheric Administration.

• Click here to visit FOXNews.com's Natural Science Center.

The whales passed under the Richmond-San Rafael Bridge on Tuesday afternoon, the last bridge along the pair's route before reaching the Golden Gate.

If the humpbacks can navigate south around the peninsula and nearby Angel Island, few obstacles would remain on their route past Alcatraz to the Pacific Ocean.

Still, the fear remained that the whales might continue south instead of west, passing under the Bay Bridge into the long southern half of the bay.

"There are lots of places they could get themselves into trouble before they go out of the Golden Gate," McInnis said.

The duo was first spotted May 13 and got as far as 90 miles inland to the Port of Sacramento before turning around.

Ariadne Green, 57, of Vallejo, came to the waterfront to catch a glimpse Tuesday after traveling last week to Rio Vista, where the whales circled for a week before heading ocean-ward.

She described the humpbacks' inland visit as a "profound spiritual experience" but was equally grateful for their departure.

"They need to go home now because their health is in jeopardy," Green said. "It's good to know they're on their way back."

Over the Memorial Day weekend, the U.S. Coast Guard had to haul several swimmers out of the water as they tried to approach the whales and fend off about 100 boats carrying would-be whale watchers.

Biologists said the saltier water where the mother humpback whale and her calf have been swimming since leaving Rio Vista has helped reverse some of the health problems caused by long exposure to fresh water.

Lesions that had formed on the humpbacks' skin over the weekend appeared to be sloughing off, California Department of Fish and Game deputy director Bernadette Fees said.

Scientists also reported that a coating of algae that was clinging to the mother farther upriver had fallen away.

Veterinarians did not get a good glimpse Monday of wounds that had been suffered by both whales and could not say whether those had started to heal, Fees said.

Antibiotics were injected into the whales on Saturday to try to slow the damage from the gashes, likely from a boat's keel.

With the whales on the move, officials did not plan to take any action to prod them toward the Golden Gate Bridge.

A convoy of boats was escorting the pair to protect them from heavy ship traffic in the bay. Bay Area ferry commuters could expect delays depending on the whales' location, Coast Guard officials said.