Isabella Sorley, 23, received a 12-week sentence yesterday after she used the web forum to verbally abuse Caroline Criado-Perez. She also told her to kill herself and said being raped was the least of her worries.
John Nimmo, 25, who was jailed for eight weeks, told Ms Criado-Perez to "shut up bitch" and suggested that he would 'find' and rape her.
Sentencing the pair at Westminster Magistrates Court, Judge Howard Riddle said it was "hard to imagine more extreme threats".
The abuse followed Ms Criado-Perez's successful campaign to get a female on a Bank of England note.
Unemployed Nimmo also targeted his abuse at Labour's Walthamstow MP Stella Creasy, describing her as a "dumb blond bitch".
The judge said the effect of the abuse on Ms Criado-Perez had been life-changing and she had been living in "panic and fear and horror".
He said of the abusive tweets: "The fact that they were anonymous heightened the fear. The victims had no way of knowing how dangerous the people making the threats were."
Nimmo, from South Shields, Tyne and Wear, and Sorley, from Newcastle- upon-Tyne, had pleaded guilty to sending menacing tweets on January 7 from 86 accounts.
Ms Criado-Perez said she did not feel able to attend yesterday's sentencing.
Writing on Twitter, she said: "I didn't feel I could cope with being in court with them - and I didn't feel sure that the judge would understand how terrifying and scarring the whole experience has been for me, which again is not something I could face.
"I feel immensely relieved that the judge clearly has understood the severity of the impact this abuse has had on me."