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The sheer numbers of cM in the range does point towards a 3C or 2C1R level as having a reasonable probability.

Does any of the matches link to any of the other matches?

In my own tree I have linked to my own matches with the relationships I quote above.

Again using my own highest cM match I have a tree of 600 build around them and 12 other cM matches linked into the tree but as yet no link to me.

My Great Grandmother’s father was unknown, then I had a high cM match that linked to an Italian family and I found a high probability who my GGGF was.  I have over 100 likely Italian Cousins and of those with trees then a specific region is common to them all.

As I wrote in my first post, do have them undertake more DNA tests with others especially Ancestry.

Thanks for both of your responses. I would love to have my mum take an Ancestry test, but she died a couple of years ago. She took a 23&me test in the past and that's what I was able to upload to My Heritage, solely in the hope to find some European matches for her.

Many of these Scandinavian relatives do match with each other in one way or another or they share common relatives between them. By looking at the shared DNA matches I'm starting to get an idea of what region(s) any potential ancestor(s) might have come from.

One point also, on the historical side and that is what are the definitions of Scandinavian  and what is the definition of German you are using.  Germany as a country was founded in 1871. 

'The German Empire was founded on January 18, 1871, in the aftermath of three successful wars by the North German state of Prussia. Within a seven-year period Denmark, the Habsburg monarchy, and France were vanquished in short, decisive conflicts.'
http://www.rootschat.com/links/01rup/

I have Danish forebears and think, by their names, that as i get further back there will be ancestors from the current-day Germany in my tree. 
This is around the Schleswig-Holstein area. 
https://en.wikipedia.org/wiki/Denmark%E2%80%93Germany_border

Sweden did also control islands in the Baltic that may have changed to German? 

Anyway the point I am making is that when looking at heritage and genetic matches we need to have some knowledge of the history of the countries.  Of course this match may be the unknown gt grandfather  you are looking for.

I appreciate the response a lot! On my paternal side I have a German family who migrated to Sweden in the 1600s and have been doing some reading on that lately.

My mother's German family, however, came from Hessen, pretty much in the middle of Germany. None of these Scandinavian matches seem to share any of her German matches for common DNA. In fact, going through shared matches, I fail to see almost any matches to other European countries. There are plenty of North Americans amongst shared matches, but no German, British, Dutch matches.

I uploaded my mother's DNA to My Heritage in the hope that it might help identify an unknown great-grandfather on her English side. Her known ancestry is half English (her mother from England), and 1/4 each Scottish and German. Matches confirm what I knew from those regions, common ancestors, etc.

However, she has an unexpectedly high number of matches from Norway and Sweden. The top matches being 62.8 cM, 54.7 cM, 46.8 cM, 45.5 cM, 42.6 cM, etc. She has at least 20 Scandinavian matches above 30 cM and over 40 more matches above 20 cM. Below that level there are obviously many more. I know that My Heritage is very popular in those countries, but these are not just a few small matches.

I’ve looked at the trees for everyone and built out trees for others and, other than very few exceptions, the matches are pure Scandinavian. The shared matches are also from those countries and some smaller North American matches.

Considering the size of some of those closest matches, and the sheer volume of matches, am I crazy for thinking that there must be a legitimate line that must be Scandinavian?

Thanks for any insight!