How to configure virtual server with web server that requires ssl certificate from clients ?

Hi Gebo , 

F5 Bigip can do this , bigip IP can give the servers the upper hand to terminate ssl connections without intervensions by using the proxy ssl feature  , look at this articles contain more details and steps to do that : 
https://my.f5.com/manage/s/article/K13385
https://techdocs.f5.com/content/kb/en-us/products/big-ip_ltm/manuals/product/bigip-ssl-administration-11-5-0/13.html

using proxy ssl leverages you : 

• The BIG-IP system to process encrypted application traffic.
• The server to retain final authority to directly authenticate and grant access to the client.
• To use the following BIG-IP system functions:
  • The iRules read or write application data.
  • The BIG-IP ASM security policy inspects and protects web application traffic.
  • The BIG-IP AAM system optimizes application traffic.
  • The system passes client certificates to servers that require mutual authentication.

I hope this helps you 🙂