Ian Brown, 44, and Daniel Dunkley, 35, died following incidents in their cells at HMP Woodhill last July.
Their relatives claim Woodhill's governor has not complied fully with Prison Service Instructions (PSIs).
But the governor and the Secretary of State say the judicial review claim is "neither appropriate or necessary".
PSIs cover management of prisoners at risk of harm to self, others and from others, early days in custody and medical emergency response codes.
Heather Williams QC, for the families, said the claim addressed the "exceptionally high" rate of self-inflicted deaths at the Milton Keynes prison.
There were seven self-inflicted deaths last year, five in 2015 and 18 at the prison since May 2013.
"The rate of self-inflicted death at HMP Woodhill is far higher than at any other prison, at a time when the suicide rate in the prison estate as a whole is at a record high," said Ms Williams.
She said the case raised serious ongoing breaches of Article 2 of the Human Rights Act, which protects the right to life, and involved long-term failures to comply with the responsibility placed on the authorities to protect prisoners.
James Strachan QC said the governor was well aware of his obligations to comply with the requirements of the PSIs.
"The defendants do not dispute that the number of deaths at the prison is a legitimate matter of concern.
"However, not only have the governor and the Secretary of State taken significant action in 2016 to improve the situation, but as the taskforce approach shows, this is a continuing high priority."
Lord Justice Irwin and Mr Justice Garnham will give their decision at a later date.

Glyndwr University is hosting the first meeting of the North Wales Cyber Security Cluster with local businesses also attending.
Prof Vic Grout said the aim is to meet monthly to share good practice.
Security agency GCHQ said people and businesses could adopt basic cyber security principals to keep safe.

The announcement comes as RAF stations in Lincolnshire celebrate their 100th anniversary.
There has been some uncertainty in recent years whether the team, based at RAF Scampton, would be retained.
Sir Michael said: "They are a key part of our defence engagement..., and I don't think the public would let us lose the Red Arrows."
There has been speculation in the media in recent years that the Red Arrows could be axed as part of defence cuts in the UK.
In 2014, The Express reported the Queen was said to be worried about the team's future.
Politicians, including Labour's Vernon Coaker, have also previously said there can be no guarantees.
Speaking to BBC Look North, Sir Michael said: "Eventually we will have to replace the aircraft, and we will start to think about that in the next year or two."
He said any attempts to axe the team is "not a fight I would have".
The Red Arrows is currently taking part in a 60-day world tour aiming to promote "the best of British", which includes its first ever display in China.
RAF Waddington, Cranwell and Scampton are all holding events marking 100 years in the county.
Sir Michael added that "Lincolnshire is central to the RAF's story, and has a proud history".
He cited the Dambusters' role in World War Two, and the Vulcan involvement in the Falklands conflict, and the work being done today to tackle terrorism in the Middle East.
RAF Cranwell is also home to the RAF's Central Flying School, which under the leadership of Robert Smith-Barry, revolutionised flight training for new pilots.
Amendment: This story was changed on November 1 to reflect the defence secretary's comments that the Red Arrows fleet would be reviewed rather than imminently replaced.
Families of two men who died in prison have brought a High Court case over the "exceptionally" high rate of self-inflicted deaths there.
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Police and experts in cybercrime are meeting in Wrexham to discuss ways to tackle the issue and keep people safe online.
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The Red Arrows aerobatic team will be "around for a while yet", Defence Secretary Sir Michael Fallon has said.