I went into the BIOS (sorry, UEFI setup) and enabled TPM, which I had read about as being one of the major issues. That wasn't enough, and I was informed that my PC still isn't compatible. I tried enabling Secure Boot, and got an error message that there was something else I had to do first (generate a security key). I figured out how to do that, and I still couldn't enable Secure Boot because my PC was in CSM mode. CSM mode is my B450 motherboard's default mode.
I tried disabling CSM mode, and then I was able to turn on Secure Boot. However, when I rebooted, my computer couldn't find my SSD, and kicked me back to the BIOS, with no message other than a beep. I turned everything off and gave up for the evening.
Then this morning I Googled some of the messages I got and realized that the problem might be that my SSD doesn't use GPT but MBR for the partition table (it was pulled from my previous PC). After thinking I was going to have to back up and recreate my hard drive, I realized that there is a command-line tool I could use, helpfully named mbr2gpt. I ran that with the appropriate options, ignoring some warnings. It ran successfully, although I got an error about my recovery image, which was spurious so far as I can tell.
Once I did all of this, I was able to switch on Secure Boot, and the compatibility checker informed me that my computer is compatible.
The point is that I'm pretty computer-savvy and have a pretty new PC. It still took me quite a while to figure this out, and a lot of people would have given up around the time they had to go mucking around in the BIOS. Unless you are have a recent store-bought PC that has Secure Boot and TPM enabled out of the box, you probably aren't going to be able to upgrade, even if your hardware is compatible.
I'm guessing that Microsoft walks back on this decision.