Where is my RDP server certificate stored?

In Windows 10

1. Search for certlm.msc in the Start Menu or using Windows key+R.
2. Click on the 'Remote Desktop' folder and then on 'Certificates'. There you will find the certificate this computer presents to its RDP clients.

In Windows 7

1. Launch mmc.exe (as an administrator).
2. 'File' -> 'Add/Remove Snap-in...'.
3. Select 'Certificates' in the 'Available Snap-ins' list and click 'Add >'.
4. A new window titled 'Certificates Snap-in' appears where you can choose from 'My user account', 'Service account' and 'Computer account'.  Choose 'Computer account', click 'Next', then 'Finish' and finally 'OK'.
5. Under the 'Console Root' folder you now have 'Certificates (Local Computer)'.
6. Click on the 'Remote Desktop' folder and then on 'Certificates'. There you will find the certificate this computer presents to its RDP clients.

You can then save this console view for easy access under 'File' -> 'Save'.

This is answered here:

It (the Remote Desktop Configuration service) [...] created the certificate. Doing so generates an event log message:

Log Name:     System
Source:       Microsoft-Windows-TerminalServices-RemoteConnectionManager 
....
Description: A new self signed certificate to be used for Terminal Server 
authentication on SSL connections was generated. The name on this certificate
is servername.domain.com . The SHA1 hash of the certificate is in the event
data.

Go to eventvwr.msc, look up events by TerminalServices-RemoteConnectionManager in System and you will get all the different times when the RDP service (re-)created its server key, along with the SHA-1 hash of each key.