Near-Threshold Computing (NTC), where the supply voltage is only slightly higher than the threshold voltage of transistors, is a promising approach to attain energy-efficient computing. Unfortunately, compared to the conventional Super-Threshold Computing (STC), NTC is more sensitive to process variations, which results in higher power consumption and lower frequencies than would otherwise be possible, and potentially a non-negligible fault rate. To help address variations at NTC at the architecture level, this paper presents the first microarchitectural model of process variations for NTC. The model, called VARIUS-NTV, extends the existing VARIUS variation model. Its key aspects include: (i) adopting a gate-delay model and an SRAM cell type that are tailored to NTC, (ii) modeling SRAM failure modes emerging at NTC, and (iii) accounting for the impact of leakage in SRAM models. We evaluate a simulated 11nm, 288-core tiled manycore at both NTC and STC. The results show higher frequency and power variations within the NTC chip. For example, the maximum difference in on-chip tile frequency is 2.3× at STC and 3.7× at NTC. We also validate our model against an experimental chip.