Phase Velocity in case of Electromagnetic Transmission
I think that phase velocity has no physical significance in this case.

The best example I can think of is "moving TV": imagine that someone moves a TV from point A to point B in front of you (from left to right), and the TV is plugged in and showing some repeated pattern moving from left to right on the screen. 

While you can state that the speed of the pattern is higher than the speed of TV (and this statement is correct), it is not really important - this pattern will not reach point B faster than TV itself.

In the above example the speed of TV (relative to you) is a group velocity. The speed of the pattern (relative to you) is a phase velocity. Phase velocity in this case may be negative (if the pattern moves from right to left and its speed on the screen is higher than the speed of TV relative to you), zero (pattern moves from right to left and its speed is equal to the speed of TV relative to you) or positive (all other cases). All these relations are also valid for a true waive packet (although negative phase velocity concept is not as simple as in this example). 

Just like the speed of the pattern is unimportant in the example (because the pattern is bound to move inside a TV repeatedly), the phase velocity is unimportant in a wave packet (because the phase is just a description of the "shape" or the "offset" of the signal inside a packet). The only thing that matters is the speed of the packet itself - its group velocity.

In slightly different words: the difference between phase velocity and group velocity shows how quickly the shape of the signal changes inside a wave packet (how quickly the pattern moves on the screen). While this speed may be calculated, its value is not really important.

While the TV example has many similarities with the real case, the speed of the pattern will never exceed the speed of light. However, this is only because both TV and the pattern are objects with mass. Imagine massless TV moving at speed of light, and massless pattern moving on the screen. In this (impossible) case you would see the pattern moving faster than speed of light.

I tried to provide an intuitive example. For equations and indeed physical and mathematical explanations you'll have to post this question in other forums (Physics, Math).

NOTE: the phase velocity is unimportant only when it is the same for all the waves in the wave packet. If phase velocity is different for different frequencies, this difference has major importance. However, even in case where phase velocities differ, the only significant information is the difference between the speeds. See the article for dispersion on Wikipedia for example.