What secrets are there for website color-management. I assumed that sRGB should be the right output.
It is. Do you have a wide-gammut monitor? When rendering sRGB on that, you need to be extra-careful - afaik a reason why pure web-devs prefer a high-quality sRGB monitor.
I'm not sure how to post an example of what I'm seeing. I can say this... I know for certain that using Firefox or Chrome yields very different results than IE for viewing... with Firefox or Chrome being much more accurate than IE.
You can enable color management in some browsers, too. Chrome seems to be broken atm, IE seems to work by default, for Firefox see this link and try again: http://ntown.at/2013/12/28/firefox-color-management
Test web pages: http://www.gballard.net/psd/go_live_page_profile/embeddedJPEGprofiles.html and http://ie.microsoft.com/testdrive/graphics/colorprofiles/default.html