An example of a perfect diamagnet is a superconductor. This implies that when a superconductor is put in a magnetic field of intensity B, the magnetic field BS inside the superconductor will be such that:

A diamagnet has a tendency to repel the magnetic field lines passing through it. For a perfect diamagnet or a semiconductor, the field lines won't enter the superconductor at all. Hence, the magnetic field inside the superconductor will be 0