Unfortunately I am not able to give you an answer as to what tiara the Princess of Wales might be wearing here. The newspaper articles I have access to are "as usual" useless when it comes to mentioning the jewels, let alone describing them with distinctive details.
From what I have been able to find out the Prince and Princess of Wales arrived to Trondheim on June 21st. That same evening the foreign Royal guests were invited to a dinner "en familie" at Their Majesties' residence Stiftsgården. The next day was the coronatin day which ended with a banquet for about 400, also at Stiftsgården.
Then followed a couple of days with even more events, like the gala concert on June 23rd and the Trondheim City Council's Souper and Ball on the 24th before terminating with a Soirée held at Stiftsgården.
So that makes potentially five glittering gala events that we know rather little about.
I really appreciate that you posted this photo Beth because at least now we have something - although we still need to find out what tiara the Princess of Wales is wearing. Hopefully somebody else can be more helpful than me in identifying the jewel.