Tests are done. Umlauts seem to get through OK, but there are issues. Characters just before an umlaut are sometimes shifted down one ASCII code, but not always.
Test 1: Audio file is tagged with Artist:
Nürnberg åäöÅÄÖ Title:
Sämre
Tags are displayed OK in Winamp
The file written by AMIP in the RDS character set, viewed in Notepad. It looks OK, it is supposed to look like this.
Same file in a Hex editor, looks OK.
Stereotool does not display the umlauts.
What it looks like in a radio display.

Characters before an umlaut are changed. N has become M, the space before å is now A with cedilla, S has become R.
Test 2:Audio file is tagged with Artist:
Nü MÜSÉk Title:
Räksmörgås
Tags are displayed OK in Winamp
The file written by AMIP in the RDS character set, viewed in Notepad. It looks OK, it is supposed to look like this.
Same file in a Hex editor, looks OK.
Stereotool does not display the umlauts.
What it looks like in a radio display.

N in
Nü has become M. The R before ä in
Räksmörgås has actually survived, but the g is now an f.
Test 3: Audio file is tagged with Artist:
Räksmörgås Title:
Nü MÜSÉk; Same as Test 2 but Artist and Title tags are swapped and a semicolon added to Title.
Tags are displayed OK in Winamp
The file written by AMIP in the RDS character set, viewed in Notepad. It looks OK, it is supposed to look like this.
Same file in a Hex editor, looks OK.
Stereotool does not display the umlauts.
What it looks like in a radio display.

Some characters before umlauts are shifted one character code down. Although the words are the same as in test 2, the changes are not the same.
The results are consistent between different runs of the same test case.
I have tested with several different RDS receivers and they all show the same in their displays.
--
Ragnar