How do I preserve True Black when saving as CMYK?

Are you saving as PSD or PDF?

If saving as PDF, make sure there is no color conversion.

First the files should be created as CMYK or convert to CMYK (Image > Mode > CMYK) -- Before creating your artwork.

The standard Black swatch in the Swatches panel is not 100% K. If you've chosen black from the Swatches panel and you click on the Foreground color swatch in the Tools panel, you will see that it has CMYK values:

Change the CMY to zero and the K to 100%. For convenience, you can add the true black swatch to the Swatches panel.

I drew the top shape with the standard black and the bottom shape with the pure black. You can see the difference in the Channels panel where the bottom shape appears only in the K channel:

If you've already drawn your artwork and don't want to redraw, target each of the CMY channels individually and delete the art from those channels so that it only shows in the K channel.