If your browser is Mozilla Firefox:
Some pages contain both secure (that is, encrypted) and insecure (unencrypted) information. If you view such a page, your browser should display a warning to this effect, and ask you if you want to continue. If you choose to continue, the padlock symbol appears with a line through it, because Firefox does not treat such pages as secure. You can still view the certificate though.
A Web site that was masquerading as the one you believe you've contacted could not fake a certificate, because no reputable CA, having checked up on them, would sign a certificate for them. And since the list of CAs in your browser includes only genuine, reputable CAs, there will be no match and your browser will reject their certificate.
However, even for the most respectable organizations, you will sometimes find warning messages on the General tab saying that in some respects the certificate is faulty. This is because some detail on the certificate is incorrect - for example, the expiry date may have passed. It is up to you to look at the details on the certificate, and decide whether you trust the Web site despite this flaw.