Over the past 50 years, a variety of instruments have obtained images of the Sun’s magnetic field (magnetograms) to study its origin and evolution. While improvements in instrumentation have led to breakthroughs in our understanding of physical phenomena, differences between subsequent instruments such as resolution, noise, and saturation levels all introduce inhomogeneities into long-term data sets. This poses a significant issue for research applications that require high-resolution and homogeneous data spanning time frames longer than the lifetime of a single instrument. As super-resolution is an ill-posed problem, multiple super-resolution outputs can explain a low-resolution input. Classical methods, such as bicubic upsampling, use only the information contained in the low-resolution image. However, in recent years it has been shown that a learning-based approach can constrain the non-trivial solution space by exploiting regularities within a specific distribution of images. In this work, we cross-calibrate and super-resolve magnetic field data obtained by the Michelson Doppler Imager (MDI); 1024×1024 px) and the Helioseismic and Magnetic Imager (HMI; 4096×4096 px). These instruments overlap from 2010 to 2011, resulting in approximately 9000 co-temporal observations of the same physical structures. Our deep learning model is trained on a subset of the overlapping data after initial pre-processing to correct for temporal and orbital differences between the instruments. We evaluate the quality of the predictive output of the model with a series of performance metrics. These metrics include the distribution of the magnetic field and physical properties captured by the signed/unsigned field. Our approach also needs to quantify the certainty of predictions to be valuable to scientists. To address this, we estimate the posterior distribution of the super-resolved magnetic field by introducing Monte Carlo dropouts on each convolutional layer.