Sony Mobile has started to roll the Android 5.1.1 Lollipop firmware update for the Xperia Z2 series in the form of build number 23.4.A.0.546. The update has only been released for carriers of the D6503 Xperia Z2 variant so far, primarily for Vodafone, however we would expect generic versions to arrive soon enough.
Likewise for the Xperia Z2 Tablet, only carrier versions of Android 5.1 have started to seed for the LTE version (SGP521). We will update this post with FTF firmware links as they become live. If you have updated, let us know how you are getting on with the update in the comments below.