How can I get the till(s) to trust the SSL certificate?

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You can manually get the till to trust the certificate. 

Go to:
https://one.yoyowallet.com/api/v3/epos
or
https://one.yoyowallet.com:4040/api/v3/epos
and follow the below steps.

1. Click the "Certificate Error" text in the address bar, and you'll see an explanation with a "View certificates" link at the bottom.
   
2. Click "View certificates” - a dialog will display information about the SSL certificate.
   
3. Click the "Certification Path" tab, and then select the top certificate shown (THIS IS CRITICAL).
   
4. Click the "View Certificate" button near the middle of the dialog. A new dialog box will open.
   
5. Click "Install Certificate", a Certificate Import Wizard will begin, which will help you install the certificate. Store the certificate into the "Trusted Root Certification Authorities”.
   
6. Click “Next" until you get to the Finish button. Once you click Finish, a final confirmation dialog (Security Warning) is displayed to make sure you want to add the new certificate (this dialog helps insure that a human is doing this action and not some malware).

Please see a complete guide here with screen shares: http://www.poweradmin.com/help/sslhints/ie.aspx