[en] A two-dimensional Heisenberg antiferromagnet with a single-ion anisotropy is studied in the presence of a uniform magnetic field along the easy axis. The concept of effective field-dependent anisotropy is applied to the theoretical description of the phase diagrams. We perform calculations using the self-consistent harmonic approximation to treat the XY phase and the Green function technique for the Ising phase. Monte Carlo simulations on LxL square lattices, with L=8,16,32 and 64, and with periodic boundary conditions were performed for the classical model. In order to test the validity of the effective anisotropy concept we compare our theoretical calculation with simulation data. We also calculate theoretically the phase diagram of the compound Rb₂MnF₄, a quasi-two-dimensional spin 5/2 antiferromagnet, finding good agreement with experimental data. Our estimates for the transition temperature of the compounds K₂MnF₄ and Mn(HCOO)₂·2H₂O, in zero magnetic field, are also in agreement with the experimental values