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The design of ungrounded meander line inductors (UMIs) and ungrounded interdigital capacitors (UICs) employed in the practical realisation of a planar ungrounded composite right-/left-handed (UCRLH) metamaterial is presented. Accurate lumped-element circuit models are proposed based on partial element theory and conformal mapping method. New and accurate analytical design formulas, for both the UMI and the UIC at very high frequency and ultra high frequency bands are derived and successfully validated through a proper comparison with the existing measurement data and the results obtained with the full wave method of moments. Further insight is sought through the investigation of the resonance mechanism of a printed dipole antenna loaded with UCRLH metamaterial cells. A prototype of the loaded dipole is fabricated to confirm and validate the theoretical calculations. The experimental results are found to be in good agreement with the theoretical calculations.