I should add that this sounds very similar to bug 308630.

Same problem here. After upgrading from kubuntu 14.10 to 15.04 is is not possible to setup a vpn connection if the certificate is not recognized. using network-manager-openconnect.
On a system running ubuntu 15.04  (also upgraded from 14.10) using  network-manager-openconnect-gnome everything works.
Problem is that under kubuntu the screen for accepting the certificate is shown but the connection is already refused. The errorlog op openconnect is the same as with Leon.
There is not even the change to provide your credentials.
==================
POST https://xxx.yyy.eu/
Attempting to connect to server xxx.xxx.xxx.xxx:443
SSL negotiation with xxx.yyy.eu
Server certificate verify failed: signer not found
SSL connection failure: Error in the certificate.
Failed to open HTTPS connection to xxx.yyy.eu
=======================================

I have the same problem here. Installed Kubuntu 15.04 from scratch & installed network-manager-openconnect (including dependencies - openconnect + vpnc-scripts)

POST https://hostx.domainy.com/
Attempting to connect to server xx.x.xx.xxx:443
SSL negotiation with hostx.domainy.com
Server certificate verify failed: signer not found
SSL connection failure: Error in the certificate.
Failed to open HTTPS connection to hostx.domainy.com

Also did not ask me for my credentials.

Versions:
vpnc-scripts (0.1~git20140806-1)
openconnect (6.00-1)
network-manager-openconnect (0.9.10.0-1ubuntu2)

Workaround - connect to VPN from command line:
$ sudo openconnect hostx.domainy.com
POST https://hostx.domainy.com/
Attempting to connect to server xx.x.xx.xxx:443
SSL negotiation with hostx.domainy.com
Server certificate verify failed: signer not found

Certificate from VPN server "hostx.domainy.com" failed verification.
Reason: signer not found
Enter 'yes' to accept, 'no' to abort; anything else to view: yes
Connected to HTTPS on hostx.domainy.com
XML POST enabled
Please enter your username and password.
GROUP: [SSL]:SSL
POST https://hostx.domainy.com/
XML POST enabled
Please enter your username and password.
Username:domain123\professorx
Password:
POST https://hostx.domainy.com/
Got CONNECT response: HTTP/1.1 200 OK
CSTP connected. DPD 30, Keepalive 20
Connect Banner:
| Notice: This system is intended solely for users authorized by ABC
| Worldwide, Inc. and related and affiliated entities ('ABC'). By
| continuing to access this system you agree to be bound by these
| terms:
| Any unauthorized use, misuse, or disclosure of information
| contained in this system may result in disciplinary action for ABC
| employees, up to and including termination of employment;
| termination of business relationship with ABC or further legal action.
| 

Connected tun0 as xx.x.xxx.xxx, using SSL
Established DTLS connection (using GnuTLS). Ciphersuite AES128-SHA.

Same problem on latest Fedora22 (Linux localhost.localdomain 4.1.3-201.fc22.x86_64).
Works on fedora 22 gnome and fedora 21 kde

log says : 
POST https://example.com/
Attempting to connect to server 146.12.36.55:443
SSL negotiation with example
Server certificate verify failed: signer not found
SSL connection failure: Error in the certificate.
Failed to open HTTPS connection to example.com
POST https://example.com/
Attempting to connect to server 146.12.36.55:443
SSL negotiation with example.com
Server certificate verify failed: signer not found
SSL connection failure: Error in the certificate.
Failed to open HTTPS connection to example.com
POST https://example.com/
Attempting to connect to server 146.12.36.55:443
SSL negotiation with example.com
Server certificate verify failed: signer not found
SSL connection failure: Error in the certificate.
Failed to open HTTPS connection to example.com

I also am having this exact same issue KDE Plasma 5.3.2 Hitting "Ok" to accept certificate will just fail

If connecting from CLI works fine:

$ sudo openconnect example.com -u user
POST https://example.com/
Attempting to connect to server 8.8.8.8:443
SSL negotiation with example.com
Server certificate verify failed: signer not found

Certificate from VPN server "example.com" failed verification.
Reason: signer not found
Enter 'yes' to accept, 'no' to abort; anything else to view: yes
Connected to HTTPS on example.com
Disabling XML POST due to authgroup option
GET https://example.com/
Attempting to connect to server 8.8.8.8:443
SSL negotiation with example.com
Server certificate verify failed: signer not found
Connected to HTTPS on example.com
Got HTTP response: HTTP/1.0 302 Object Moved
GET https://example.com/+webvpn+/index.html
SSL negotiation with example.com
Server certificate verify failed: signer not found
Connected to HTTPS on example.com
Please enter your username and password.
GROUP: [Group-A|Group-B]:Group-A
Password:
POST https://example.com/+webvpn+/index.html
Got CONNECT response: HTTP/1.1 200 OK
CSTP connected. DPD 30, Keepalive 20
Connected tun0 as 10.0.8.69, using SSL + deflate
Established DTLS connection (using OpenSSL)

*** This bug has been confirmed by popular vote. ***

I have same problem in archlinux with plasma5. Even if openconnect in command line works fine and trusts to server sertificate, Network Manager doesn't work.

I have the same problem in Kubuntu 15.10 (Plasma 5.4.2).

I have the same problem after upgrading to Kubuntu 15.04 (from Kubuntu 15.10)

sorry, to 15.10 from 15.04 of course

Found the reason, why vpn didn't work after the upgrade!
After the upgrade, the user certificate file is also used for the CA certificate!

Hi @Leon

After upgrade openSUSE distro 13.2 -> Leap 42.1 i have got similar problem (plasma-nm5-openconnect-5.4.2).
The VPN server to which I am  trying to connect, has an untrusted certificate (self-signed) and in addition its CN does not match the hostname.

POST https://my-vpn-server
Attempting to connect to server my-vpn-server-ip:443
SSL negotiation with centaur1.visiona.com
Server certificate verify failed: signer not found
SSL connection failure: Error in the certificate.
Failed to open HTTPS connection to my-vpn-server

To get around this, I added the untrusted certificate in the edit VPN in "CA Certificate" (first saving it as a .cer by with some HTML browser)

I have tested your link https://dept-ra-cssc.vpn.wisc.edu/
and it work for me.

POST https://dept-ra-cssc.vpn.wisc.edu/
Attempting to connect to server 144.92.42.108:443
SSL negotiation with dept-ra-cssc.vpn.wisc.edu
Connected to HTTPS on dept-ra-cssc.vpn.wisc.edu
Got HTTP response: HTTP/1.1 200 OK
Content-Type: text/html; charset=utf-8
Transfer-Encoding: chunked
Cache-Control: no-cache
Pragma: no-cache
Connection: Keep-Alive
Date: Sun, 08 Nov 2015 16:28:14 GMT
X-Frame-Options: SAMEORIGIN
X-Aggregate-Auth: 1
HTTP body chunked (-2)
XML POST enabled

I am getting a dialogue to select a group and enter a user name and password.

To me it looks like in your system (some truststore / cacerts) lack Root CA that issued the certificate for "InCommon RSA Server CA". Analyzing the certificate chain it would be "USERTrust RSA Certification Authority". Try download certificate from https://dept-ra-cssc.vpn.wisc.edu/  and add that certificate (the path to .cer) at set up a VPN connection.

Some problem on Debian Stretch.

I fix that with next steps:
1. apt-get install cinammon
2. apt-get install network-manager-openconnect-gnome
3. Create new VPN connection in GUI
4. That work
5. Change session to Plasma
6. At now, network-manager with openconnect work fine.

Git commit 42f0cbd57677cde47d671774fc099c33ab749c7e by Jan Grulich.
Committed on 02/12/2015 at 08:25.
Pushed by grulich into branch 'master'.

Revert: avoid using dialog->exec() in openconnect VPN plugin

We need to wait for the dialog result before we continue

M  +9    -11   vpn/openconnect/openconnectauth.cpp

http://commits.kde.org/plasma-nm/42f0cbd57677cde47d671774fc099c33ab749c7e

Git commit 77282d889333d558e805ef744627d567cf9816e9 by Jan Grulich.
Committed on 02/12/2015 at 08:26.
Pushed by grulich into branch 'Plasma/5.5'.

Revert: avoid using dialog->exec() in openconnect VPN plugin

We need to wait for the dialog result before we continue

M  +9    -11   vpn/openconnect/openconnectauth.cpp

http://commits.kde.org/plasma-nm/77282d889333d558e805ef744627d567cf9816e9