I want to have a shield hang in the air in front of the player’s face for a second as part of a boss melee combat move. This RL combat move prevents the target from seeing the next shot coming.

I did this in oblivion using set a lot of trig and set position functions each 0.05 second via a script. With Skyrim I do not think this will work well and even if it did would be a little too heavy on the resources.

Is there a function that can do this “automatically”? That keeps an object in a fixed distance to the player and relative to the player’s z position?

You could try equipping an item of apparel into one of the player's unused slots, and set its mesh to be a shield in front of the wearer's face. That's the only thing I can think of at the moment. It wouldn't look very convincing, though .