  We demonstrate the presence of parity-time (PT) symmetry for the
non-Hermitian two-state Hamiltonian of a dissipative microwave billiard in the
vicinity of an exceptional point (EP). The shape of the billiard depends on two
parameters. The Hamiltonian is determined from the measured resonance spectrum
on a fine grid in the parameter plane. After applying a purely imaginary
diagonal shift to the Hamiltonian, its eigenvalues are either real or complex
conjugate on a curve, which passes through the EP. An appropriate basis choice
reveals its PT symmetry. Spontaneous symmetry breaking occurs at the EP.
