Version:           3.4.92 (using KDE 3.4.92 (beta2, >= 20051010), compiled sources)
Compiler:          gcc version 3.3.4 20040623 (Gentoo Linux 3.3.4-r1, ssp-3.3.2-2, pie-8.7.6)
OS:                Linux (i686) release 2.6.11-gentoo-r7

From ~/.xsession-errors:
khtml (part): 0x83c92a0 urlSelected: complete URL:https://bestilling.certifikat.tdc.dk/pocesselfservice/jsp/login.jsp target=
kdeinit: Got EXEC_NEW 'kio_http' from launcher.
kdecore (KLibLoader): WARNING: KLibrary: /usr/lib/libcrypto.so.0.9.7: undefined symbol: PKCS7_content_free
kdecore (KLibLoader): WARNING: KLibrary: /usr/lib/libcrypto.so.0.9.7: undefined symbol: OpenSSL_add_all_algorithms
kdecore (KLibLoader): WARNING: KLibrary: /usr/lib/libcrypto.so.0.9.7: undefined symbol: OpenSSL_add_all_algorithms_conf
kdecore (KLibLoader): WARNING: KLibrary: /usr/lib/libcrypto.so.0.9.7: undefined symbol: OpenSSL_add_all_algorithms_noconf
DCOP: register 'anonymous-27509' -> number of clients is now 37
kded: [int NetworkStatusModule::status(const QString&)]  no networks have status for host 'https://bestilling.certifikat.tdc.dk/pocesselfservice/jsp/login.jsp'
kdecore (KNetwork resolver): shouldResInit: /etc/resolv.conf updated
DCOP: register 'anonymous-27509' -> number of clients is now 38
no networks have status for host 'https://bestilling.certifikat.tdc.dk/pocesselfservice/jsp/login.jsp'
kio (KRun): ERROR: 0x8652540 ERROR (stat) : 24 Connection to host bestilling.certifikat.tdc.dk is broken.

However, if I enter 'konqueror https://bestilling.certifikat.tdc.dk' in a shell, it starts with no hazzle.