The security certificate is nothing to do with your end, it's held on the server. The organisation that sipplies them can be a pain and the process of obtaining a new one can be slow, but.... there is no reason why the company you are dealing with shouldn't have sorted it out.
The certificate really just tells you that the person you are dealing with might not be the one you think it is, in other words the certificate they are using doesn't conform to the server it was initially issued to. If you are confident the company is OK then it is fine to carry on using the site.