When passing Mach 1, the nose shock wave moves rearwards, and passes over the static ports.
As a result, there is a "twitch" on both the altimeter (barely visible) and on the VSI (verical speed indicator, very visible) when exceeding Mach 1.
To further complement the answer, Concorde's static ports are mounted on much bigger plates than usually seen. This is because in supersonic flight the static pressure is peculiarly sensitive to the actual angle of the skin around the 'hole' relative to freestream. Consequently the ports are set in plates that have been machined flat. These plates were then jig-set to accurate angles relative to body datum.
CL