The pair who pleaded guilty to sending abusive tweets to a feminist campaigner are due to be sentenced on January 24 at Westminster Magistrates' Court.
John Nimmo was released on conditional bail while Isabella Sorley was remanded in custody.
District Judge Howard Riddle warned Sorley it was "almost inevitable" that she would receive a jail sentence.
He told Nimmo, described to the court as a "social recluse", that "all options" remained open.
The feminist campaigner who received abuse on Twitter said she was "hugely relieved" that defendants John Nimmo and Isabella Sorley have pleaded guilty.
Caroline Criado-Perez tweeted: "This is not a joyful day, these two abusers reflect a small drop in the ocean, both in terms of the abuse I received across July and August, but also in terms of the abuse that other women receive online.
"I hope that for some people who are watching, this conviction will be a warning: online abuse is not consequence-free".
Ms Criado-Perez added that she will stay off Twitter as much as possible today "as inevitably the renewed attention will mean renewed abuse".
Feminist campaigner Caroline Criado-Perez "suffered life-changing psychological effects" from the abuse she received on Twitter following her successful campaign to get a woman on British banknotes, a court heard.
Prosecutor Alison Morgan told Westminster Magistrates' Court, "In particular, the menacing nature of the tweets sent by both defendants caused her significant fear that they would find her and carry out their threats."
Ms Criado-Perez received abusive messages "of one type or another" from some 86 Twitter accounts, including those accounts attributed to defendants John Nimmo and Isabella Sorley.
Nimmo and Sorley have pleaded guilty to sending "menacing" tweets to Ms Criado-Perez.
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.
John Nimmo, 25, from South Shields and Isabella Sorley, 23, from Newcastle-upon-Tyne, pleaded guilty today at Westminster Magistrates' Court to sending "menacing" tweets to feminist campaigner Caroline Criado-Perez.
Tony Wang, the general manager of Twitter in the UK, said the company had "engaged with the relevant parties" over complaints of online harassment against a feminist campaigner.
An option to report abuse from within Twitter apps and websites would be launched soon, he suggested:
A man arrested on suspicion of Twitter harassment was bailed this afternoon, police said earlier.
A man arrested on suspicion of Twitter harassment offences has been bailed until September, police said.
- Complaints of crimes involving Facebook and Twitter increased by 780% in four years, according to official police figures from 29 British forces
- The phenomenon of social networking crime was comparatively minor in 2008 when 556 reports were made. Last year this figure stood at 4,908
Twitter said it plans to include a button for reporting abuse within every tweet, amid a growing furore over online threats to rape and kill a feminist campaigner.
A high-profile feminist who has experienced abuse on Twitter told ITV that the social networking site needs to enforce its own terms of service and acknowledge there is a problem.