Usually Web Client is published through internet and therefore you will require CA-Signed certificate for more security. VMware changed the locations of SSL certificates in version 5.1. Here I am summarizing the steps of installing CA-Signed certificate:
1. Generate your CSR and obtain the CA-Signed certificate. I am not touching this part since there are many ways to generate the CSR and I believe its simple to do so.
2. Once the new certificate is obtained (should be in pfx format), you need to copy the certificate, private key, and root certificate into the following path C:\ProgramData\VMware\vSphere Web Client\ssl.
3. Navigate to C:\Program Files\VMware\Infrastructure\vSphereWebClient\server\config. From there, you need to edit the file tomcat-server.xml to include the path of the new certificate as well as the pass-share for the certificate.
Note: This file is protected and not editable. You need to copy it, edit the copied version, delete "tomcat-server.xml" and rename the copied edited version to "tomcat-server.xml"
4. Once done, restart Web Client service.