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Quantization is an effective technique to reduce memory footprint, inference latency, and power consumption of deep learning models. However, existing quantization methods suffer from accuracy degradation compared to full-precision (FP) models due to the errors introduced by coarse gradient estimation through non-differentiable quantization layers. The existence of sharp local minima in the loss landscapes of overparameterized models (e.g., Transformers) tends to aggravate such performance penalty in low-bit (2, 4 bits) settings. In this work, we propose sharpness- and quantization-aware training (SQuAT), which would encourage the model to converge to flatter minima while performing quantization-aware training. Our proposed method alternates training between sharpness objective and step-size objective, which could potentially let the model learn the most suitable parameter update magnitude to reach convergence near-flat minima. Extensive experiments show that our method can consistently outperform state-of-the-art quantized BERT models under 2, 3, and 4-bit settings on GLUE benchmarks by 1%, and can sometimes even outperform full precision (32-bit) models. Our experiments on empirical measurement of sharpness also suggest that our method would lead to flatter minima compared to other quantization methods.