Judge Howard Riddle said the effect of Twitter abuse on feminist campaigner Caroline Criado-Perez had been "life-changing".
The victim describes "panic and fear and horror," he said.
The judge added that online abuse aimed at Stella Creasy had also had a "substantial" impact on the Labour MP, who has had a panic button installed in her home.
– Judge Howard Riddle
The fact that they were anonymous heightened the fear.
The victims had no way of knowing how dangerous the people making the threats were, whether they had just come out of prison, or how to recognise and avoid them if they came across them in public.