shadow boxes

Shadow boxes functions as both noun and verb.

A shadow box is a shallow, framed display case with a glass front, used to exhibit memorabilia, medals, or small collectibles arranged in three-dimensional compositions: He kept his military ribbons in a shadow box.

To shadow box is to throw punches at an imaginary opponent, a training technique for boxers.

Figuratively, shadow boxing describes fighting something intangible or going through the motions of conflict without real engagement: The candidates spent the debate shadow boxing rather than addressing issues.