Coordinate networks like Multiplicative Filter Networks (MFNs) and BACON offer some control over the frequency spectrum used to represent continuous signals such as images or 3D volumes. Yet, they are not readily applicable to problems for which coarse-to-fine estimation is required, including various inverse problems in which coarse-to-fine optimization plays a key role in avoiding poor local minima. We introduce a new coordinate network architecture and training scheme that enables coarse-to-fine optimization with fine-grained control over the frequency support of learned reconstructions. This is achieved with two key innovations. First, we incorporate skip connections so that structure at one scale is preserved when fitting finer-scale structure. Second, we propose a novel initialization scheme to provide control over the model frequency spectrum at each stage of optimization. We demonstrate how these modifications enable multiscale optimization for coarse-to-fine fitting to natural images. We then evaluate our model on synthetically generated datasets for the the problem of single-particle cryo-EM reconstruction. We learn high resolution multiscale structures, on par with the state-of-the art. Project webpage: https://shekshaa.github.io/ResidualMFN/.