Addendum to Ian Co's "Steps to Install ImageMagick for Windows" specifically for Uniform Server Z and how to fix if you get an empty list of ImageMagick supported formats):
Thanks to Ian Co's comments above for setting me in the right direction.
My Uniform Server is installed to B:\UniServerZ, adjust the following steps to your specific installation.
If you've been messing around with a gazillion solutions like me, first delete any previous copies of imagemagick dll-s (i.e. IM_MOD_RL...dll-s, CORE_RL...dll-s) from your sysem, i.e. I had copied them to C:\Windows\system, B:\UniServerZ\core\php56, B:\UniServerZ\core\php56\extensions.
1. Download ImageMagick-6.8.9-1-vc9-x86.zip from http://windows.php.net/downloads/pecl/deps/
Extract contents of bin folder to B:\UniServerZ\core\php56 (or whichever vresion of php you are using)
2. Download the appropriate imagick package from http://pecl.php.net/package/imagick/3.1.2/windows
For me the right one was php_imagick-3.1.2-5.6-ts-vc11-x86.zip , check phpinfo whether you need the thread-safe version or not and which architecture.
Extract php_imagemagick.dll ONLY (and not the other dll-s) to B:\UniServerZ\core\php56\extensions
Previously I had tried ImageMagick-6.9.3-7-vc11-x86.zip and ImageMagick-6.9.3-7-vc14-x86.zip but the dll-s here did not work, perhaps because Uniform Server was compiled using VC9? and these were compiled with later versions!? What a mess.
I had also tried creating a C:\ImageMagick and adding it to PATH user-level and to MAGICK_HOME system-level environment variables, but this proved unnecessary (although it also works).
Also, installing the windows binary releases from
http://www.imagemagick.org/script/binary-releases.php#windows
was unnecessary (and might actually mess things up if windows tries those dll-s first).