Cannot capture (HDMI) output of Graphics Card with BlackMagic UltraStudio
What solved the problem:

Check your capture software settings. All settings (your monitor/capture device settings, your hardware settings and the settings in your capture software) should be correct and equal.

What can help track down similar issues:

Very likely a framerate issue. Only the 4K version of the Blackmagic Capture cards supports 60FPS and your monitor is or was probably set to 60Hz or 50Hz, though your capture card probably is only supporting 30FPS @ 1080p (assuming thats your resolution). (Edit: In this case not true, the UltraStudio (4k) does support 60fps even at 4k over SDI but if someone else has this issue, have a look at the specs of your capture card)

Assuming your are using Windows go to the resolution settings and click on advanced settings after selecting the capture card "display" and then go to the "Monitor" tab and select a lower refresh rate like 30FPS or 25FPS. Then set the same refresh rate in your capture settings.

On a Mac you can use a tool called SwitchResX to change your refreshrate or alternatively in your case simply set your capture settings to the output settings shown in the System Informations for the Capture Card "display". So same resolution and refresh rate.

If your really unlucky your Mac doesn't recognize the UltraStudio as a display or the Ultrastudio isn't sending any EDID information, though I somewhat doubt that's the case. I had this issue all the time with the 4K PCI-E capture card from Blackmagic, it always was a settings mismatch.

Also make sure that if you want to capture a video that's playing back, it isn't protected by HDCP like Jim Mack suggested.