The problem with SSDs is that the control system on the SSD can map sectors and writing to a file or disk block does not mean that the data from that block is gone. Retrieving data orphaned in this way is very difficult, would require removing memory chips from the board and then dumping the contents, then being able to reconstruct the drive data, then the filesystem layer.
ShredOS uses an updated version of the program that DBAN uses. If you have a Linux system you can use these directly. shred is also a command line tool that will erase a file, disk partition or physical disk. But only as far as the controller allows this to happen.
The ATA command set also includes commands to erase data blocks, but these are not consistently implemented, and may not give any indication of success or failure.
As @Andrew_Gabriel mentions above that best option is to use full disk encryption from the start so erasing the key effectively erases the data, and you never need to worry about orphaned sectors.