When will Endnote X4 for Mac be compatible with Word for Mac 2011? In the meantime, how can one manage?
According to their website:


  EndNote X4 is not compatible with Word 2011. The compatibility of Word 2011 with EndNote X4 will be addressed in a free update. Please register your software to be informed when EndNote X4 is compatible with Word 2011.


On their message board, this message says:


  The schedule has changed since then so I cannot provide a firm ETA, other than we're now targeting the first quarter of 2011.


From the later comments in that thread (and other threads in their forum), there appear to be a lot of unhappy customers.

Your other options appear to be:


Use X4 with MS Word 2008 (and thankfully, you can run 2008 and 2011 apps at the same time)
Use X4 with Pages '09
Use X3 with MS Word 2011
Apply to beta test the Word 2011 version of X4
Don't use Endnote; instead just use Word 2011's built-in tools