The phenomena of macroscopic quantum tunnelling and coherence of the Néel vector are investigated for small single-domain antiferromagnetic particles. Both the Wentzel-Kramers-Brillouin exponents and the pre-exponential factors are found exactly for the tunnelling rates, for various forms of the magnetocrystalline anisotropy. The calculations are performed on the basis of the two-sublattice model and the instanton method applied to the spin-coherent-state path integral.