Crews located the Cessna but could not immediately say whether the pilot was also found, Contra Costa County sheriff's spokesman Jimmy Lee said.
The search began Sunday afternoon after the Cessna 210 and a Hawker Sea Fury TMK 20 collided in mid-air.
The pilot of the vintage airplane landed safely, but the Cessna crashed into the water.
The names of the pilots haven't been released. The National Transportation Safety Board is investigating.
An NTSB official will be interviewing the pilot of a plane that made it back to land and reviewing the pilots' backgrounds, agency spokesman Terry Williams said.
The collision occurred near the Richmond-San Rafael Bridge.
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.
Debris was found in the bay after the collision.
The Sea Fury's pilot landed at Eagle's Nest Airport in the small city of Ione in Amador County, Federal Aviation Administration spokesman Ian Gregor said. The Sea Fury's occupants — a husband and wife —were uninjured. It was unclear how many people were in the Cessna.
U.S. Coast Guard helicopters and vessels conducted search patterns in the bay on Monday, Lt. Joshua Dykman of the U.S. Coast Guard said.
Both planes had departed from Eagle's Nest Airport to participate in the Pacific Coast Dream Machines, an annual festival at Half Moon Bay Airport that features a variety of planes, motorcycles and cars. Both planes left Half Moon Bay, about 20 miles south of San Francisco, and were on their return flight.
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.