1960s. South Africa. Miriam Makeba
In 1963, after an impassioned testimony before the United Nations Committee Against Apartheid, all Makeba's records were banned in South Africa. 
Miriam Zenzile Makeba began her professional career in 1950, when she joined the Johannesburg group the Cuban Brothers. She came to national prominence during the mid-1950's as a member of local leading touring group, the Manhattan Brothers. Her starring role in an American film-maker's documentary, 'Come Back Africa', got her an invitation to attend the film's premiere at the Venice Film Festival in spring 1959, and while in Italy, she privately decided not to return home. Shortly afterwards her South African passport was withdrawn.
In London after the Venice Festival, Makeba met Harry Belafonte, who offered to help her gain an entry visa and work permit to the United States of America, along with the usual guest appearances on television and jazz clubs. Miriam Makeba was later on said to be blacklisted from the US music industry for her marriage to Black Panther leader Stokely Carmichael.
Makeba returned to South Africa in 1990 at the end of apartheid after spending 30 years in exile.
Miriam Makeba said she felt terrible about being exiled, especially when she could not return to South Africa to bury her mother.
 
Sources:
panafricannews.blogspot.com, allafrica.com and rasputinmusic.com

1960s. South Africa. Dolly Rathebe
Legal restrictions and curfews made it very difficult for black entertainers to work in South Africa. Censorship meant that jazz was played less on the government broadcasting network, the authorities favouring “native styles” which supposedly presented a less sophisticated picture of black culture. She gave up singing, making a living from running a shebeen through the hard years of the 1970’s and 1980’s.
Source: www.workersliberty.org

1960s. South Africa. Dorothy Masuka
Dorothy Masuka song ‘Dr. Malan’ which included the line “Dr. Malan has difficult laws…” earned the attention of South Africa's feared Special Branch, which paid Masuka a visit and promptly banned the record. When she sang for Lumumba, the fallen hero of Congolese independence, in 1961, the Special Branch seized the master and all copies of the record they could find.
Source: www.afropop.org

1960s. Zimbabwe. Stella Chiweshe and Beuler Djoko
Stella Chiweshe began learning to play the mbira dza vadzimu (thumb piano) in 1964. It was very unusual for a girl to play mbira at that time, and Chiweshe had to face the dissaproval of her community where woman performers were often treated as "loose women". In the same way Beuler Djoko.
Source: Banning Eyre: ‘Playing with fire’, published by Freemuse, p. 40-41

1960-1990. South Africa. National anthem
‘Nkosi Sikele Africa’ (also spelled ‘Nkosi Sikelel 'lAfrica’, meaning "God bless Africa") was sung for many years during the anti-apartheid struggle while singing it publicly was a criminal offense. Nkosi Sikele Africa was written in 1897 and officially adopted by the African National Congress in 1925. ANC was banned after the Sharpeville massacre in 1960 and as the song became an anthem of the liberation struggle against apartheid in the country, it was banned by the South African government. But it was still sung quietly behind closed doors.
When South Africa became a democracy in 1994, the song was adopted as the national anthem.
"Every time we sing it, there is something it does in our spirits. We believe it even shakes our ancestors where they are resting. This is a song that's a prayer when you listen to the lyrics, but the tune and the way it was sung from the beginning gave people so much power," Mazibuko from the famous vocal group Ladysmith Black Mambazo once said. A lyrical excerpt from ‘Nkosi Sikele Africa’:

Bless our efforts
Of union and self-uplift
Of education and mutual understanding
And bless them
Lord, bless Africa
Blot out all its wickedness
And its transgressions and sins
And bless it