Merkel and Ardern could be seen as the mother and daughter of MMP, and Ardern said they might exchange views on MMP and coalitions.
It took almost six months for Merkel to put together the current government in Germany - a grand coalition between Merkel's centre-right Christian Democratic Union and the centre-left Social Democratic Party.
"I'd say I have a more straightforward situation than hers if the coalition negotiations was anything to go by," Ardern said.
However, the experienced Merkel may be able to give Ardern tips on managing tricky coalition partners.
Ardern has had a few thorny issues to deal with since entering Government as she manages the often diametrically opposed personalities and politics of NZ First and the Greens. But Merkel has now headed three so-called "grand coalitions". Those are governments made up of the two biggest parties in Parliament.
Ardern might also get some tips on how to haul in Trumpesque egos such as Shane Jones and Winston Peters.
Merkel has managed to make it clear when she believed Trump needed reining in, from eye-rolling when he remarked both had been spied on in common, to a sharp comment that she would miss Obama, to comments about how the days Europe could count on the US were over.
She has called him out on everything from the "trade wars" tariffs, to the withdrawal from the Paris Agreement on climate change.
The European Council is expected to agree to the mandate for negotiations to begin in May.