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For the first time, an automated design procedure based on space mapping techniques is developed for the EM-based optimization of left-handed coplanar waveguide (CPW) filters based on split ring resonators (SRRs). Our design procedure is based on a constrained Broyden-based input multistage space mapping strategy, using a statistical approach to parameter extraction (PE). Pre-conditioning of the coarse model design parameters is used at each PE iteration, imposed by the severely bounded region of validity of the equivalent circuit model. The space mapping algorithm effectively aligns equivalent circuit responses with simulated results provided by full-wave electromagnetic simulation tools. Our method is illustrated by the EM-based design of a CPW bandpass filter with 3 SRRs.