By considering the 3-3-1 and the left-right symmetric models as low energy effective theories of the trinification group, alternative versions of these models are found. The new neutral gauge bosons in the universal 3-3-1 model and its flipped versions are considered; also, the left-right symmetric model and the two flipped variants of it are also studied. For these models, the couplings of the $Z'$ bosons to the standard model fermions are reported. The explicit form of the null space of the vector boson mass matrix for an arbitrary Higgs tensor and gauge group is also presented. In the general framework of the trinification gauge group, and by using the LHC experimental results and EW precision data, limits on the $Z'$ mass and the mixing angle between $Z$ and the new gauge bosons $Z'$ are imposed. The general results call for very small mixing angles in the range $10^{-3}$ radians and $M_{Z'}$ > 2.5 TeV.