Please add support for TLS Server Name Indication (see RFC4366 [1]) to w3m. This is necessary for virtual hosting for https sites under many circumstances (esp. for servers shared by individuals that each own a domain, so there cannot be a single certificate). There's additional information available on Wikipedia [5].
velox.ch provides a test server [2-4].
Both OpenSSL and GnuTLS support SNI, so it's only a matter of w3m signalling the requested hostname to the library.
OpenSSL support for SNI doesn't seem to documented yet, but should be enough easy to factor out from the included example SSL client (apps/s_client.c - search for "tlsext").
For GnutTLS, add a call to gnutls_server_name_set() seems to suffice. [6]
[1] http://www.ietf.org/rfc/rfc4366.txt
[2] https://alice.sni.velox.ch/
[3] https://bob.sni.velox.ch/
[4] https://carol.sni.velox.ch/
[5] http://en.wikipedia.org/wiki/Server_Name_Indication
[6] http://www.gnu.org/software/gnutls/manual/gnutls.html#TLS-Extensions
File Added: w3m-0.5.2-sni.patch
Simple (but complete) patch for TLS SNI support