Have you changed the SSL certificate? Maybe the certificate has expired. Just press on "Add Exception" and continue to access your website anyway.

Firefox is giving me a connection error about the certifacate

What is the exact error?

What is the website URL?

You can retrieve the certificate and check details like who issued certificates and expiration dates of certificates.

• Click the link at the bottom of the error page: "I Understand the Risks"

Let Firefox retrieve the certificate: "Add Exception" -> "Get Certificate".

• Click the "View..." button and inspect the certificate and check who is the issuer of the certificate.

You can see more Details like intermediate certificates that are used in the Details pane.

If "I Understand the Risks" is missing then this page may be opened in an (i)frame and in that case try the right-click context menu and use "This Frame: Open Frame in New Tab".

• Note that some firewalls monitor (secure) connections and that programs like Sendori or FiddlerRoot can intercept connections and send their own certificate instead of the website's certificate.
• Note that it is not recommended to add a permanent exception in cases like this, so only use it to inspect the certificate.

If you can't inspect the certificate via "I Understand the Risks" then try this:

Open this chrome URI by pasting or typing this URI in the location/address bar to open the "Add Security Exception" window and check the certificate:

• chrome://pippki/content/exceptionDialog.xul

In the location field type/paste the URL of the website

• retrieve the certificate via the "Get certificate" button
• click the "View..." button to inspect the certificate in the Certificate Viewer

You can inspect details like the issuer and the certificate chain in the Details tab of the Certificate Viewer. Check who is the issuer of the certificate.