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
European court says US-EU treaty allowing transfer of personal data by US companies is invalid due to privacy fears.
Luxury car maker Lexus has made a full-size driveable 'Origami car' out of cardboard to celebrate the craftsmanship of their workers.
Who will get hired and who will get fired by Lord Sugar in this year's Apprentice?