The results of searches for B-(s)(0) -> J/psi p (p) over bar and B+ J/psi p (p) over bar pi(+) 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 sigma significance is seen for the decay B-(s)(0) -> J/psi p (p) over bar and an upper limit on the branching fraction is set at the 90% confidence level: B(B-(s)(0) -> J/psi p (p) over bar) < 4.8 x 10(-6), which is the first such limit. No significant signals are seen for B-0 -> J/psi p<(p)over bar> and B+ -> J/psi p (p) over bar pi(+) decays, for which the corresponding limits are set: B(B-0 -> J/psi p (p) over bar) < 5.2 x 10(-7), which significantly improves the existing limit; and B(B+ -> J/psi p<(p)over bar>pi(+)) < 5.0 x 10(-7), which is the first limit on this branching fraction.