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 other plane involved made it safely to a nearby airport 40 minutes after the crash. Two people aboard, a husband and wife, were not injured, the county's Undersheriff Jim Wegner said.
The two planes, a single-engine Cessna 210 and a single-engine Hawker Sea Fury TMK 20, were heading home from 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.
The Associated Press contributed to this report.