Anthony Lancaster, from Circular Road, Creggan, Sharon Rafferty and Anthony McDonnell claimed the increased obligation to provide advance notification was irrational, unfair and a breach of human rights.
But a judge ruled that the amended regime is a legitimate and proportionate attempt to deal with the threat from terrorism.
Mr Justice Scoffield said: “There remains a cohort of determined terrorist offenders in this jurisdiction who are intent on threatening life, limb and property.
“The State is entitled, indeed required, to take steps to mitigate against the murderous intent of terrorist organisations and would-be terrorist offenders.”
All Registered Terrorist Offenders (RTOs) must provide the PSNI with a range of personal information, including details of planned travel outside the United Kingdom.
Amendments within the Counter-Terrorism and Border Security Act 2019 introduced an increased obligation to give seven days advance notification of any intention to cross the border, regardless of purpose or time to be spent in the Republic of Ireland.
Lawyers for the three RTOs took a judicial review against the Home Office and the PSNI to challenge the lawfulness of the enhanced requirements.
In 2015 Anthony Lancaster, 60, received a suspended sentence at Belfast Crown Court for acting as master of ceremonies at a 32 County Sovereignty Movement.
He was convicted of assisting in arranging or managing a meeting to be addressed by a person who belonged or professed to belong to a proscribed organisation.
The offence related to his role at an Easter Rising commemoration in April 2012.
Lancaster claimed the new requirements interfere with his private and family life by deterring him from making short trips to Co Donegal for sporting events and other purposes.
Similar arguments were made on behalf of Sharon Rafferty and Anthony McDonnell.
In 2014 Rafferty, 47, from Pomeroy, Co Tyrone, received an eight-year sentence for offences including possession of a firearm and preparation of terrorist acts in connection with a dissident republican training camp.
McDonnell, with a previous address in the Ballymurphy area of west Belfast, was convicted of five counts of having information likely to be of use to terrorists in December 2013.
The 53-year-old Irish citizen had been found to be in possession of security force members’ vehicle registration details.
He served half of a three years and six months sentence in custody before being released on licence, but remained subject to the notification requirements for a 10-year period.
Counsel for the Home Office and the PSNI argued that the amended regime is a necessary and proportionate response to the grave danger posed by terrorist activity.
The alleged impact has been overstated by the three RTOs, it was contended, with their grounds of challenge based on hypothetical scenarios, conjecture, and an unwillingness to properly engage with the requirements.
Backing those submissions, Mr Justice Scoffield held that the monitoring and modified obligations had an important legitimate aim.
“The need for such measures is in my view heightened where a border may be crossed with ease and with otherwise limited risk of detection or knowledge on the part of the authorities, all the more so where this is an established feature of the operations of terrorist organisations,” he said.
The judge added: “The protection of the public from terrorist campaigns requires some restriction on qualified (European) Convention rights, all the more so in respect of those who have been convicted of serious terrorist offences.”
Dismissing all grounds of challenge, Mr Justice Scoffield said RTOs “cannot be assumed to be model citizens”.
He added: “It is a depressing fact that those convicted of serious terrorism offences may become more radicalised or determined, rather than rehabilitated, by the sentences imposed upon them. Continued vigilance is required.
“As the authorities show, given the difficulty in predicting risk in this area, a precautionary approach is not only appropriate but required.”
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