  Preparing and certifying bound entangled states in the laboratory is an
intrinsically hard task, due to both the fact that they typically form narrow
regions in the state space, and that a certificate requires a tomographic
reconstruction of the density matrix. Indeed, the previous experiments that
have reported the preparation of a bound entangled state relied on such
tomographic reconstruction techniques. However, the reliability of these
results crucially depends on the extra assumption of an unbiased
reconstruction. We propose an alternative method for certifying the bound
entangled character of a quantum state that leads to a rigorous claim within a
desired statistical significance, while bypassing a full reconstruction of the
state. The method is comprised by a search for bound entangled states that are
robust for experimental verification, and a hypothesis test tailored for the
detection of bound entanglement that is naturally equipped with a measure of
statistical significance. We apply our method to families of states of $3\times
3$ and $4\times 4$ systems, and find that the experimental certification of
bound entangled states is well within reach.
