In my view, the uncertainty principle in quantum mechanics appears because of the importance of wave mechanics in telling particles how to move. So we should view the uncertainty principle as coming from wave mechanics (which is also what Chris Hillman and Tim Thompson are saying, but from the point of view of the pure mathematics underneath wave mechanics-- we must also observe physically that wave mechanics has a place at the physical table, which also means that Fourier transforms become a relevant way to understand dynamics of particles). Note that as soon as we say the uncertainty principle is an expression of wave mechanics, then the door opens to point to any macroscopic wave phenomenon, and identify that as a macroscopic example of the uncertainty principle, applied to the elementary excitations that comprise that macroscopic wave phenomenon.

For example, the fact that your radio can pick up signals from an emitting tower through a window, even when your eye cannot see the tower through that window, is a classic example of the uncertainty principle-- the size of the window gives you some knowledge about the lateral constraints about the location the photons would have to move through, so that imprints an uncertainty onto their lateral momentum. The excitations of visible light are particles with much higher momenta then the radio counterparts that your radio detects, so the same imprinted uncertainty in lateral momentum translates into a very small angle of uncertainty in the direction of the light particles' motion, but a much larger angle of uncertainty in the direction of the radio-wave excitations. At some point the angle of uncertainty in the direction of the radio waves exceeds the angular width of the window, and at that point it is no longer necessary for the location of the radio tower to conform to the window's angular acceptance in order for the radio photons to get to your radio, i.e., you can hear from a tower you can't see. The short term for all that is "diffraction".