Yes, it is strange seeing the Sun get lower without setting. (Assuming it isn't too cloudy to see the Sun at all!) But you don't have a longest day on the June solstice in the far north. For example, in Tromsø (northern Norway) the last sunrise was on May 18th and it won't set again until July 26th (and then for about 45 mins). So you can see this effect through the summer.
Last summer I was in Norway and once we got far enough north, the Sun didn't set for four days. Moving back south, on the fifth day we had
two sunsets. This picture of
"the Midnight Sun" was taken several days before the solstice. And it was actually the One-O'Clock-in-the-Morning Sun.