We calculate the conductance through rings with few sites L described by the t-J model, threaded by a magnetic flux Φ and weakly coupled to conducting leads at two arbitrary sites. The model can describe a circular array of quantum dots with large charging energy U in comparison with the nearest-neighbor hopping t. We determine analytically the particular values of Φ for which a depression of the transmittance is expected as a consequence of spin-charge separation. We show numerically that the equilibrium conductance at zero temperature is depressed at those particular values of Φ for most systems, in particular at half filling, which might be easier to realize experimentally.