<p>This theoretical modeling and simulation paper presents design and projected performance of broadband and resonant non-volatile Variable Optical Attenuators (VOAs), based upon the LNOI-SiN photonic platform and operating at 1550&#xa0;nm. These compact devices facilitate the integration of on-chip Microwave Photonic links in the LNOI-SiN platform, by controlling the optical carrier-sideband ratio. The proposed VOAs consist of a programmable multilevel directional coupler (broadband) and microring resonator (resonant). The devices are based on SiN-strip-loaded LNOI waveguides with a thin layer of phase-change material (PCM), specifically GSST, as the programmable region of the waveguided structure. The electrically induced phase change of the PCM, applied by means of segmented graphene-based microheaters, allows the realization of the phase matching and the phase mismatching between two coupled waveguides when the material phase of GSST is changed between amorphous and crystalline. By controlling the number of the activated graphene-based microheaters, we demonstrate that a digitally controlled non-volatile power attenuation at the output of the device can be induced. In the manuscript, optical and thermal simulations of the devices are shown to demonstrate the feasibility of the devices, revealing an insertion loss lower than − 2 dB and dynamic range larger than 15 dB. The proposed VOAs represent useful devices to ensure the stability and performance of complex optical networks, where miniaturization, low-power and digital control are required.</p>