I found an interesting post on the Postman Blog, which was almost correct. For easy reference, I give the correct approach here:
You can easily make any HTTP SOAP request using Postman by following these simple steps:
1. Give the SOAP endpoint (not necessarily the WSDL) as the URL. If you use a WCF service hosted on Azure that would be a .svc endpoint like https://dsponrampservice.azurewebsites.net/DSPOnRampService.svc
2. Set the request method to POST.
3. Add Authorization as required.
4. On the Body tab, select Raw and body type “text/xml”
5. Now go to the header tab. You will allready see two headers: Authorization and Content-Type. You will have to add a header named SoapAction manually. You can get the Soap Header of the operation from the WSDL. For Instance: http://sap.com/xi/WebService/soap1.1.
6. Click [Send] to call the operation.
In the above mentioned post, it’s indicated that you should specify the name of the operation in the body. In my case I had a service with just one operation, so maybe that’s the reason I didn’t have to. As a side note. After adding the operation in the message, I got a serialization exception. So, I still think you should add the operation name in the body.