Mr Riddle ruled on Friday that the 87-year-old former Board of Deputies president should appear in person, even if he could not understand proceedings or respond to questions.
The ex-MP was not in court to hear more than an hour of legal argument over the severity of his condition.
He is likely to be charged with more than 20 counts relating to allegations of historic child sex abuse dating back to the 1960s, 1970s and 1980s .
Evidence had been given by two expert dementia consultants as part of Lord Janner's defence case.
Lawyers met on Tuesday morning to discuss how he could be brought to court, but his defence team announced the challenge to Mr Riddle’s decision.
Lord Janner's family has said he is "entirely innocent", and the peer denies any wrongdoing.
