The easiest way (if possible under Norwegian constitution) would be for Märtha Louise herself to not ask for approval or for her to give up her rights to the throne upon/before marriage. What is the official process for asking for approval (is only the king involved; or also parliament - as some referenced the Storting?)
When it was the heir (i.e. Haakon), he talked with the King before his engagement, then the King informed the Prime Minister and the Storting that he would give his consent.
But in Märtha's case, they are treating it quite differently.
Because when the newspaper Aftenposten (after the engagement in June 2022) asked the court whether the Prime Minister had been consulted, they said the following:
''Som Hans Majestet Kongen har vært tydelig på tidligere så bestemmer ikke Kongeparet hvem prinsesse Märtha Louise skal gifte seg med. Det er prinsessens eget valg. Det er for øvrig ingen krav om at Kongen må ha samtale med statsministeren om dette.''
''As His Majesty the King has made clear in the past, the Regent-Couple doesn't decide whom Princess Märtha Louise marries. It's the princess' own choice. Furthermore, there is no requirement that the King must have a conversation with the Prime Minister about this.''
You must have an account to read the article (
link).
And the Prime Minister's office confirmed to the tabloid VG that the King and the Prime Minister had not discussed Märtha's engagement and said that there is no requirement for them to do so.
They also said that the Prime Minister had congratulated Märtha and Durek on their engagement and wished them all the best.
You must have an account to read the article (
link).
In the same article, you can also read that the President of the Storting, Masud Gharahkhani said that the Storting was not notified by the Palace about the engagement.
''Given her formal status, it is also not something we would expect'', he said.
So the court, the government and the Storting are all treating this as if it's not that important at all.
And I'm reading this as: Yes, the King will give his consent, but she is not going to be monarch, so it's not a big deal!
and is there a way to give up rights to the throne (preferably without her daughters losing their rights as well) except for entering into an unapproved marriage?
No, but Märtha can just ask the King not to give his consent and then make it publicly herself that it is her own wish. But then her daughters would lose their succession rights. But who knows, perhaps the government could come up with a solution so they can keep it.
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If Princess Märtha Louise is no longer in the line of succession... Wil she be then a Princess still?
Well, article 34 in the constitution pre-1990 said the following: ''The nearest heir to the throne, if he is the son of the reigning King, shall bear the title of Crown Prince. The other persons entitled to succeed to the throne shall be called Princes,
and the Royal daughters, Princesses.''
(BTW, the bolded stuff in my translation differs a bit from the one you can read in Tatiana Maria's post, which is written by the Norwegian historian Dag T. Hoelseth)
Article 34 after 1990, when women were allowed to succeed: ''The King shall make provisions concerning titles for those who are entitled to succeed to the Crown.''
This means that only those with succession rights can bear a royal title.
But it was decided back in 1990 that Princesses Ragnhild and Astrid (who were not in line to the throne) should be allowed to keep their titles since they had gotten them before the changes of article 34 took place.
Read more in this article from the Scandinavian University Press (
link).
And who knows, perhaps Märtha, like Ragnhild and Astrid, would have been allowed to keep her title since she had gotten it before the changes of article 34 took place.