In terms of suggestions of music similar to Trentemoller, or which might differ but appeal to Trentemoller fans, I guess "similar" depends on which aspect of his music is the main draw for an individual. I can appreciate some people like Trentemoller, but don't really like "dance music" per se. The other thing being format preference and whether a person wants to avoid buying 12 inch singles. I'm assuming here that CD would be the preferred format, but if anyone is interested in collecting 12s who doesn't already buy this stuff I could waffle on further
I suppose from the electronic dub and "minimalist" tech angles, obvious suggestions would be Basic Channel label/group
http://www.basicchannel.com/ (Rhythm and Sound, etc.). If you don't tend to buy 12s, then this CD is well worth getting
http://basicchannel.com/item/RSD-1
From the minimalist "techno" angle, then I'd highly recommend a lot of Carl Craig's material, or mixes, some really sublime music.
[Almost forgot - Jeff Mills!!]
From the same angle, Sandwell District's output is also well worth seeking out. CD format being by far the cheapest route
http://www.juno.co.uk/ppps/products/407038-01.htm
Expect to pay c.£100 for that on vinyl.
Slightly different UK slant (not really sure what genre you'd apply) I highly recommend exploring Actress. Splazsh on CD being a good start point. Straying away from Trentemoller a little so may be more or less up your street.
http://www.juno.co.uk/ppps/products/392668-01.htm
Another on Honest Jon's label artist/group - Moritz Von Oswald Trio. Sort of soundscape, meets jazz, meets... er.. some other thing
http://www.juno.co.uk/ppps/products/417533-01.htm
Not sure whether it would be straying too far from the Nordic soundscape aspect, but I would recommend at least checking out Shackleton, Peveralist, Appleblim, Midland, Ramadanman and similar, if only to form an opinion.
Good Shackleton mixed CD (all his material)
http://www.juno.co.uk/ppps/products/411711-01.htm
Three EPs (but on CD
http://www.juno.co.uk/ppps/products/368753-01.htm
From the Berghain / deep techno angle - Ben Klock's and Marcel Dettmann's output or mixes. This Ben Klock mix CD is a decent start point:
http://www.juno.co.uk/ppps/products/392029-01.htm
Another on Ostgut Ton label, an unmixed CD with a variety of good individual tracks:
http://www.juno.co.uk/ppps/products/403069-01.htm
A CD of Dettmann produced music:
http://www.juno.co.uk/ppps/products/388127-01.htm