Robert: It's hosted by 1and1.com and I went and logged on to change my credit card number (got a new card). They had an announcement that basic certification was now provided for their hosted sites. So I clicked a few buttons etc. and it was done. No changes to the web site code itself was needed.
But you need to alter the FTP logon to access your data, the old URl etc. need altering. All spelled out nicely, only took a few minutes.
Now if 1and1.com hadn't done all the grunt work, I'd have had no idea how to do this.