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Arrays of superconducting quantum interference devices (SQUIDs) are highly sensitive magnetometers that can operate without a flux-locked loop, as opposed to single SQUID magnetometers. They have no source of ambiguity and benefit from a larger bandwidth. They can be used to measure absolute magnetic fields with a dynamic range scaling as the number of SQUIDs they contain. A very common arrangement for a series array of SQUIDs is with meanders as it uses the substrate area efficiently. As for most layouts with long arrays, this layout breaks the symmetry required for the elimination of adverse self-field effects. We investigate the scaling behavior of series arrays of SQUIDs, taking into account the self-field generated by the bias current flowing along the meander. We propose a design for the partial compensation of this self-field. In addition, we provide a comparison with the case of series arrays of long Josephson junctions, using the Fraunhofer pattern for applications in magnetometry. We find that compensation is required for arrays of the larger size and that, depending on the technology, arrays of long Josephson junctions may have better performance than arrays of SQUIDs.