A seal assembly includes a first component, a second component, a first seal, a first shelf, a second shelf, and a second seal. The second component is adjacent to the first component and forms a cavity between the first and second components. The first seal spans the cavity. The first shelf extends axially from the first component and is located between the first seal and a hot gas path. The second shelf extends axially from the second component and is located between the first shelf and the hot gas path; the second shelf together with the first shelf forms a flow channel. The second seal conforms to the first shelf, sealing the flow channel.