So much useful information, thanks alot for the replies, I appreciate it.
@Hugo Morvan
The seedlings I have are from Redwood National Park. I don't know how old the seedlings were when I got them, but I remember them being about 7-8 inches tall at the time. So they have spent a fair bit of time in their natural habitat and been exposed to their native soil. However, they've been in ordinary gardening soil ever since they migrated to Scandinavia. I will do some detective work in the morning and phone up botanical gardens in and around Stockholm, like you said.
I find it somewhat mind-boggling that only one of the two trees is showing signs of distress. The other one seem perfectly healthy with its bright green needles intact, no drying or discolouration - yet. Could it be pests or disease?
Since yesterday I've started to moisten the needles and covering the trees with plastic bags for a few hours, as suggested. I've thought of repotting the distressed tree, in case it has outgrown its rather small container. But I also fear I might fall into the trap of loving them to death by doing too much, as I imagine amateurs like myself often do.