Looks like wildcard certificates do work okay. The problem is that MfE is not following the certificate chain (which the server makes available). I have to extract & load the immediate parent CA certificate in order for MfE to work.
cmcli -T common-ca -v <your-server-dns-name-or-ip-address>:<port-number>
cmcli -t ssl-ca -v <your-server-dns-name-or-ip-address>:<port-number>
0115e5345e4dd64855ed1e3d44060be25f26c2e6 nixu-jum trust chain(1): b5567d6c9eef05f07966d98eb2a85716bff4e80d Maemosec test CA Verified OK
0115e5345e4dd64855ed1e3d44060be25f26c2e6 nixu-jum Verification failed: self signed certificate