Get Windows to recognize it first. Open Device Manager: Rt-Clk [Start], select Device manager. At the top-left, is your computer name, Rt-Clk on it , then left click on "Scan for hardware changes". If it isn't listed after the scan, connect to a different USB port.
I agree with what Ed Convery stated. I use a Logitech WebCam C930e and have not had an issue. Maybe let us know what WebCam you are using as I have a few different ones I have used in the past. Maybe try rebooting the computer after you unplug the WebCam and then try plugging it back in and opening Camtasia and see if it recognizes it or not. You could also try another software app like OBS which is free or if it came with it's own software see if it works in those and let us know. Thanks for posting and have a great day/night.