As with any upgrading technology (QC10-11-11.52-12, etc., or even with general file backup media/storage 8'', 5.25'', 3.5'' floppy, USB flash, or magnetic tape - remember tape?), if you want archive something, you need to move it onto the newer technology first. Even then, sometimes later, you need to go back an upgrade it again (pull it up to the new technology).

So, unfortunately, you will need to UPGRADE the old projects to be ''archived'' to the new QC/ALM format/version, confirm they upgraded (spot check), then de-activate or REMOVE from QC Site Admin. If you De-activate, they will be ''out-of-sight'' for all users, but will be seen within Site Admin Tool in the ''project tree''.
You could consider first moving them to some other domain like ''Archival'' before de-activating - yet another layer to show that they are archived.

Now, you would still have a DB/schema and repository/files corresponding to each various project that is ''archived''. These may be confusing to DBA's or System admins and will possibly take up space in various backups nu-necessarily, BUT you can easily do a RESTORE with the DBID.xml file in the project's repository folder any time it is needed.

If they are small enough (total size DB+repository < 2.5GB), you can do a project EXPORT to a QCP file and they can be re-imported as needed. Remember, QCP files also are VERSION-specific, so, if creating an archival QCP, the QCP filename should have QC version in it as a reminder. You could store your archival QCP's (named so they make sense and including QC version in name) somewhere you can find them easily. When you upgrade QC/ALM again, these would need to be imported to their appropriate QC/ALM version, then upgraded again and dumped back out to new QCP's for the newer QC/ALM version. Eventually, you may want to totally ''retire'' some very old projects and stop upgrading them.