Firm swordfish steaks hold up well on the grill or broiler. These swordfish steaks are nicely flavored with a lemon and olive oil sauce. The sauce is brushed over the fish as it cooks. While swordfish is nutritious and delicious, it does have a high level of mercury. The us fda and epa advise that women who may become pregnant, pregnant women, nursing mothers, and young children avoid eating fish high in mercury. They advise this group to completely avoid swordfish, shark, tilefish, and king mackerel.