Many real-world settings require registration of a pair of medical images that differ in spatial resolution, which may arise from differences in image acquisition parameters like pixel spacing, slice thickness, and field-of-view. However, all previous machine learning-based registration techniques resample images onto a fixed resolution. This is suboptimal because resampling can introduce artifacts due to interpolation. To address this, we present RealKeyMorph (RKM), a resolution-agnostic method for image registration. RKM is an extension of KeyMorph, a registration framework which works by training a network to learn corresponding keypoints for a given pair of images, after which a closed-form keypoint matching step is used to derive the transformation that aligns them. To avoid resampling and enable operating on the raw data, RKM outputs keypoints in real-world coordinates of the scanner. To do this, we leverage the affine matrix produced by the scanner (e.g., MRI machine) that encodes the mapping from voxel coordinates to real world coordinates. By transforming keypoints into real-world space and integrating this into the training process, RKM effectively enables the extracted keypoints to be resolution-agnostic. In our experiments, we demonstrate the advantages of RKM on the registration task for orthogonal 2D stacks of abdominal MRIs, as well as 3D volumes with varying resolutions in brain datasets.