  We use numerical transfer-matrix methods, together with finite-size scaling
and conformal invariance concepts, to discuss critical properties of
two-dimensional honeycomb-lattice Ising spin-1/2 magnets, with couplings which
are antiferromagnetic along at least one lattice axis, in a uniform external
field. We focus mainly on the shape of the phase diagram in field-temperature
parameter space; in order to do so, both the order and universality class of
the underlying phase transition are examined. Our results indicate that, in one
particular case studied, the critical line has a horizontal section (i.e. at
constant field) of finite length, starting at the zero-temperature end of the
phase boundary. Other than that, we find no evidence of unusual behavior, at
variance with the reentrant features predicted in earlier studies.
