Finally discovered how to do this. Here is how to use a second monitor in portrait mode:
Open System Preferences from your iMac dock.
Click Displays - Click Arrangement - Click Gather Windows - the secondary monitor dialog box opens.
Click Rotation - Click 90 degrees rotation for PORTRAIT MODE.
Click CONFIRM on the secondary monitor to keep Portrait mode.
Select the desired resolution. I chose 1200 x 1920.
You'll see a dialog box that says, "About to change the display mode."
Click Confirm. (If it appears. For some resolutions, I did not have to click confirm, most likely because the monitor supports those resolutions.)
Then resize the windows of the software you're using.