I appreciate this is an OLD OLD post, but this is still a problem.
Zombie does not connect to a working, open and verified https port with an untrusted certificate. Curl, wget and the browser itself do connect to the same connection.
Setting process.env.NODE_TLS_REJECT_UNAUTHORIZED = "0" doesn't solve the problem. I don't know if this is a problem with Zombie or with the underlying jsdom (I guess either is possible), but this is THE top result for a search of "Zombie https ECONNREFUSED" and you didn't even attempt to answer the problem. Do you have any further insight in the 3 years that have passed since the question was first asked?
Cheers,