Debris was found in San Pablo Bay after the 4:05 p.m. collision near the Richmond-San Rafael Bridge, but there were no signs of the downed pilot, Coast Guard Petty Officer Loumania Stewart said.
The collision involved a single-engine Cessna 210 and a single-engine Hawker Sea Fury TMK 20, Federal Aviation Administration spokesman Ian Gregor said.
The Cessna crashed into the water and the Sea Fury's pilot was able to land 40 minutes later at Eagle's Nest Airport in the small Northern California city of Ione, Gregor said.
Amador County firefighters and medics sent to the Ione airport were not needed because the pilot and passenger in the Sea Fury — a husband and wife — were not injured, the county's Undersheriff Jim Wegner said.
Both planes had departed from Eagle's Nest Airport to participate in the Pacific Coast Dream Machines, an annual festival in Half Moon Bay that features a variety of planes, motorcycles, and cars. Both planes left Half Moon Bay Airport, about 20 miles south of San Francisco, and were on their return flight to Ione.
Witnesses at Point San Pablo Yacht Harbor told the San Francisco Chronicle that the Cessna spiraled out of control and crashed into the choppy water after the collision.
"Everyone associated with the Pacific Coast Dream Machines Show is terribly saddened by this news and we hope and pray the missing plane and survivors are found," the event organizers said in a statement.
Wegner wouldn't discuss damage to the Sea Fury, citing the ongoing investigation by the FAA and the National Transportation Safety Board.
FAA records indicate the Sea Fury, a vintage British fighter plane, is registered to Sanders Aeronautics Inc. in Ione. A man who answered the phone at the company's listed number declined to comment.
Sanders Aeronautics' website said the family-run company specializes in aircraft restoration and brothers Dennis and Brian Sanders are avid air racers.