Using a sample of [Formula: see text] events collected with the BABAR detector at the PEP-II storage ring, we search for the electroweak penguin decays B+→ K+e+e-, B+→ K+μ+μ-, B0→K*0e+e-, and B0→ K*0μ+μ-. We observe no significant signals for these modes and set preliminary 90% C.L. upper limits of [Formula: see text]