Wrong Portal proxy settings lead to webservice call failure

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Symptom
An Enterprise Portal application is trying to perform a web service call but it fails with exception such as:
com.sap.engine.services.webservices.jaxm.soap.accessor.NestedSOAPException: Problem in server response: Proxy Authentication Required.com.sap.engine.services.webservices.jaxm.soap.accessor.NestedSOAPException: IOError while working with the message. Check the nested Exception.
And the nested exception is one of the following:Caused by: java.io.IOException: Proxy responded: HTTP/1.1 400 Bad RequestCaused by: java.net.ConnectException: Connection [...]

How to configure ws clients HTTP proxy for the J2EE engine

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Symptom
An external server can not be reached from within the engine.
An example would be when the generation of IGS-based graphics fails.
Other terms
IGS, graphics, broken pipe, proxy, web service clients
Reason and Prerequisites
A proxy server is configured for the web service clients deployed on the J2EE engine, but certain URLs can not be reached by this [...]

Additional information for SAP.Net Connector

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Symptom
Additional information for SAP.Net Connector that was not included in the guide.
Other terms
SAP .NET Connector, Proxy Wizard
Solution
SAP.NET Connector Version 1.0 has been available since Nov 21, 2002. You can download the software from http://service.sap.com/connectors.
Version 2.0 is also available. Use only the new version for new developments.
Report any problems with the SAP.NET Connector under the components:
BC-MID-CON-DNW [...]