We report on self-suspended micro-resonators patterned in Z-cut lithium niobate on insulator substrates. The fabrication technique consists of two single steps, focused ion beam milling for the micro- and nano-structuring and subsequent SiO2 etching for the realization of thin self-suspended membranes. The fabrication process of a free-standing photonic crystal cavity and a suspended micro-disk is described and the linear and nonlinear optical properties of the micro-resonators are investigated at telecommunication wavelengths. The whispering gallery modes of the micro-disk are measured experimentally and compared to an analytical model. The fundamental transverse-electric polarized mode of the photonic crystal cavity is measured and compared to three dimensional finite difference time domain simulations. Second harmonic generation enhancement due to the field confinement in the cavity mode is demonstrated. These results are promising for the use of Z-cut lithium niobate self-suspended membranes as platforms for highly efficient miniaturized photonic devices for telecommunication applications.