She had supporting roles in the war story Battle Hymn (1957) with Rock Hudson and in the drama Mister Cory (1957) with Tony Curtis, directed by Blake Edwards. She was featured in Kelly and Me, a comedy with Van Johnson, and as Cornelia Bullock in the 1957 remake of My Man Godfrey with David Niven. In 1958, Hyer appeared in a Playhouse 90 televised version of Reunion by Merle Miller, along with Frances Farmer. She next appeared in Paris Holiday (1958) with Bob Hope and Houseboat (1958) with Cary Grant. Hyer was the foil for soon-to-be TV icons Dan Rowan and Dick Martin of Rowan & Martin's Laugh-In fame in their Once Upon a Horse... (1958) Western film by Hal Kanter. For the 1958 drama Some Came Running, directed by Vincente Minnelli, Hyer was nominated for the Academy Award for Best Supporting Actress. Soon after, she had supporting roles in The Big Fisherman (1959) and The Best of Everything (1959) with Joan Crawford. Also in 1959 Martha played the role of Hannah Haley in Rawhide (TV series) S1 Ep 8 Incident West Of Lano. Hyer started the 1960s with a supporting role in Ice Palace (1960), a drama with Richard Burton, and The Last Time I Saw Archie (1961), a comedy with Robert Mitchum. Next she was in A Girl Named Tamiko (1962), Wives and Lovers, and The Carpetbaggers (1964). By 1964, Hyer had turned 40 and after a decade of success, began having trouble finding good roles, and worked mainly in television and in European and American B-films. She did appear in two episodes of The Alfred Hitchcock Hour, ('"A Piece Of Action" in 1962 and "Crimson Witness" in 1965). Also in 1965, she was in The Sons of Katie Elder, a Western with John Wayne and Dean Martin. She guest-starred on the television series Bewitched as Margaret Marshall, a wealthy, seductive woman. In 1966, she was in The Chase, directed by Arthur Penn and starring Marlon Brando and Robert Redford. On television, she guest-starred on The Beverly Hillbillies in the episode "The Richest Woman", in which she plays Tracy Richards, the world's richest woman. In the late 1960s, she starred in the film drama Some May Live, the crime comedy The Happening, and the suspense film Crossplot. In 1967, she guest-starred on Family Affair in the episode "Star Dust", in which she plays Carol Haven, a movie star.