Both planes had been at a show Sunday in Half Moon Bay on the Pacific Coast south of San Francisco, officials said. They were returning to Eagle's Nest Airport in Ione, Calif., about 50 miles east of the Bay area, when they collided over San Pablo Bay near Richmond shortly after 4 p.m.
A 1965 Cessna 210 with only the pilot on board crashed into the bay. Search teams found debris from the plane but no sign of the pilot, the Coast Guard said.
The other plane, a Hawker Sea Fury TMK 20, landed in Ione about 40 minutes later. Two people, a husband and wife, were on board and both were unharmed.
The Sea Fury is a restored British fighter from the early 1950s. The plane is registered to Sanders Aircraft Inc. and was restored by Frank Sanders, the father of the company's present owners, who was killed in a 1989 crash.
The planes had been at the Dream Machine show, which features motorcycles and cars as well as planes.