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Superconducting thin-film metamaterial resonators can provide a dense microwave mode spectrum with potential applications in quantum information science. We report on the fabrication and low-temperature measurement of metamaterial transmission-line resonators patterned from Al thin films. We also describe multiple approaches for numerical simulations of the microwave properties of these structures, along with comparisons with the measured transmission spectra. The ability to predict the mode spectrum based on the chip layout provides a path towards future designs integrating metamaterial resonators with superconducting qubits.