If someone knows the WPA2 password to your Meraki mesh network, and you want to block them, you can’t. The block function only works on the public network. Meraki’s Jeff Gould explains in an email to me:

The blocking function works only on the public network. There is no blocking capacity on the private Meraki Network. There are a variety of folks who would like to have this functionality and I believe that we will have features to address this in 2009.

Wow. So, like, sometime this year? That’s kind of vague.

Right now, it seems the only way to keep someone that knows your password off your network is to change your password.