Quantization reduces the precision of deep neural networks to lower model size and computational demands, but often at the expense of accuracy. Fully quantized models can suffer significant accuracy degradation, and resource-constrained hardware accelerators may not support all quantized operations. A common workaround is selective quantization, where only some layers are quantized while others remain at full precision. However, determining the optimal balance between accuracy and efficiency is a challenging task. To this direction, we propose SeQTO, a framework that enables selective quantization, deployment, and execution of ONNX models on diverse CPU and GPU devices, combined with profiling and multi-objective optimization. SeQTO generates selectively quantized models, deploys them across hardware accelerators, evaluates performance on metrics such as accuracy and size, applies Pareto Front-based objective minimization to identify optimal candidates, and provides visualization of results. We evaluated SeQTO on four ONNX models under two quantization settings across CPU and GPU devices. Our results show that SeQTO effectively identifies high-quality selectively quantized models, achieving up to $54.14$% lower accuracy loss while maintaining up to $98.18$% of size reduction compared to fully quantized models.