There’s several pieces to SSL and Zen Cart. Of course, you need a secure certificate. Do note whether it works with both www and non-www. If it does not, be sure to only use the one that works. (Yes, I know that seems simplistic but details matter.)
Next, there are two places in the files where the change needs to take place – both of them config files, one for the customer facing part and one for admin. Both are located in the includes directories and titled configure.php. The examples here are from a 1.5.5 site. 1.5.4 is a little different but not by much.
Notice that there are three changes needed to fully change to SSL. 1) add the s to the HTTP_SERVER, 2) add the s to the HTTPS_SERVER and 3) change ENABLE_SSL from false (or blank) to true.
On the admin side, it’s simpler.
Change the HTTP_SERVER and add the s at the end of the http inside the apostrophes. Really, that’s it for admin. The entries below that are actually just for the catalog if you are clicking on the Storefront link in admin. Those changes are the same as the actual configure file in the catalog side.
SEO notes:
Once you’ve done that, adding in a redirect is advised so that folks cannot use the http without it redirecting to https. I won’t go into details on why this should be done and I dang sure don’t want to try to explain as it’s tricky. This post addresses that but I can promise you that what works depends on several things – including your server. I suggest contacting your hosting support team for help. https://wiztech4zc.com/blog/htaccess-redirects-for-seo/