When I try to access meta.*.stackexchange.com via HTTPS, I get a warning:

meta.codegolf.stackexchange.com uses an invalid security certificate.

The certificate is only valid for the following names:

*.stackexchange.com, stackexchange.com, meta.stackexchange.com, stackoverflow.com, *.stackoverflow.com, stackauth.com, sstatic.net, *.sstatic.net, serverfault.com, meta.serverfault.com, superuser.com, meta.superuser.com, stackapps.com, openid.stackauth.com, *.meta.stackexchange.com

(Error code: ssl_error_bad_cert_domain)

I'm using HTTPS Everywhere, but disabling it for Stack Exchange prevents me from logging in to the aforementioned meta sites—I simply get dropped back without being logged in (also, trying to ask a question causes a redirect loop).

Adding a security exception does work, though. Maybe this is because I'm already logged in to other Stack Exchange sites via a secure connection?

Update: It appears disabling the entry for Stack Exchange in HTTPS Everywhere then logging out and logging in again solves the problem of not being able to log in. See balpha's answer for details.