SSD upgrade for 2013 21" iMac?
It seems there is a workaround for this. One can buy an external Thunderbolt SSD, and set up a Fusion Drive. Since Thunderbolt is extremely fast, this is a low cost, low work solution that is very suitable for desktop machines like the iMac.

There are a lot of guides online on how to set up the disks.

It boils down to 


Backing up your machine using Time Machine
Install OS X onto a third external drive.
Boot from said drive.
Create fusion drive over external SSD and internal HD.
Reboot from fusion drive and re-install OS X, restore from Time Machine


Maybe one can skip the install to external HD, since newer Macs come with Internet Recovery. This would save quite a bit of work.

Once in recovery, you can see your disks using diskutil list. Let's say you see the disks disk1s2 (internal HD, OS X partition) and disk2 (clean SDD).

Now you can create the Fusion Drive:

sudo diskutil cs create [ArbitraryName] disk2 disk1s2
sudo diskutil cs createVolume [UUID] jhfs+ [ArbitraryName] 100%


The output of the first command results in a UUID which you use in the second command.

After this, you should be able re-install or restore OS X onto the Fusion Drive.

I haven't tried this yet, it is merely a summary of the linked article! So be careful and make backups!