The results of searches for B0(s)→J/ψ pp¯ and B + → J/ψ p p¯ π+ decays are reported. The analysis is based on a data sample, corresponding to an integrated luminosity of 1.0 fb−1 of pp collisions, collected with the LHCb detector. An excess with 2.8 σ significance is seen for the decay B0s→J/ψ pp¯ and an upper limit on the branching fraction is set at the 90 % confidence level: B(B0s→J/ψ pp¯) < 4.8 × 10−6, which is the first such limit. No significant signals are seen for B 0 → J/ψ p p¯ and B + → J/ψ p p¯ π + decays, for which the corresponding limits are set: B(B0→J/ψ pp¯) < 5.2 × 10−7, which significantly improves the existing limit; and B(B+→J/ψ pp¯π+) < 5.0 × 10−7, which is the first limit on this branching fraction.