Richard's workaround above:
Setting
Page.ClientTarget = "uplevel"
in thePage_Init
event.
is the correct one; you need to disable the use of User-Agent sniffing to get ASPNET to send IE11 the proper script blocks. http://msdn.microsoft.com/en-us/library/system.web.ui.page.clienttarget.aspx
Unfortunately, it turns out that the patch they took to enable IE10 doesn't work properly with IE11 (because the IE team significantly changed the IE user agent string, removing the MSIE token by default). So, another patch for ASP.NET was shipped in June 2013. See https://stackoverflow.com/a/18651133/126229