John Nimmo and Isabella Sorley pleaded guilty to sending "menacing" tweets to a feminist campaigner following her successful campaign to ensure a woman features on British banknotes.
Nimmo, 25, and Sorley, 23, admitted a charge of sending the messages in July last year to Caroline Criado-Perez.
The pair sent the tweets after Bank of England Governor Mark Carney revealed that Pride and Prejudice author Jane Austen would replace Charles Darwin as the face of the £10 note.
The announcement was hailed as a "brilliant day for women" by Ms Criado-Perez.
More top news
The Serious Fraud Office has been fined £180k after confidential documents from a high-profile investigation were sent to the wrong person.
British hopes for a sunny Easter break have been dealt a blow with forecasters warning of a week of wind, rain and even snow.
More than one in five school staff have had a false allegation made against them by a pupil, according to a survey.