Below is a part of the text from the EMET 5.1 User Guide (page 13-14):
EMET has reporting capability provided through a Windows Service called Microsoft EMET Service. Once EMET is installed, the service is set to automatically start with Windows. The EMET Service is responsible to dispatch the EMET Agent, which will show
up in the system tray area of the taskbar with an EMET icon. The visibility of the EMET Agent icon in tray area can be configured via Group Policy or via the command line tool).
The EMET Service performs the following tasks:
Write events in the Windows Event Log: EMET events are...
Show important events via a tooltip in the taskbar notification area: Similar in severity to the error messages written to the Windows Event Log, when EMET stops an exploit due to one of the mitigations or detects an untrusted SSL certificate,
a message is displayed for the user, stating which application is being stopped and which mitigation has been used to stop the exploit. In case of a Certificate Trust violation, it shows details about the untrusted SSL certificate on the current HTTPS connection.
...
However it seems that EMET does not always shows a notification and the logged information is not always the same.
stefancpt clarified that the lack of the EMET notification occurs when the user doesn't have administrative rights. See also (t)his
post!