In numerous contexts, high-resolution solutions to partial differential equations are required to capture faithfully essential dynamics which occur at small spatiotemporal scales, but these solutions can be very di cult to obtain using traditional methods due to limited computational resources. A recent direction to circumvent these computational limitations is to use deep learning techniques for super-resolution, to reconstruct high-resolution numerical solutions from low-resolution simulations. The proposed approach, the Super Resolution Operator Network (SROpNet), frames super-resolution as an operator learning problem and draws inspiration from existing architectures to learn continuous representations of solutions to parametric differential equations from low-resolution approximations, which can then be evaluated at any desired location. In addition, no restrictions are imposed on the spatiotemporal sensor locations at which the low-resolution approximations are provided, thereby enabling the consideration of a broader spectrum of problems arising in practice.