This paper presents a method to determine the effective permittivity (ε) and permeability (μ) of electromagnetic metamaterials from reflection and transmission coefficients. The analysis is performed on structures composed of periodic arrangements of wires, split ring resonators (SRRs), and combinations of both. The recovered frequency-dependent ε and μ are consistent with analytic expressions predicted by effective medium arguments. A wire medium exhibits a frequency region where the real part of ε is negative, while SRRs produce a frequency region where the real part of μ is negative. In the combined structure, at frequencies where both ε and μ have negative real parts, the real part of the refractive index is also negative. The method involves using transmission and reflection coefficients (S-parameters) calculated for a wave incident on a finite slab of metamaterial. The scattering data is inverted to determine the refractive index (n) and impedance (z), from which self-consistent values for ε and μ are obtained. The technique is applicable to experimental characterization of metamaterial samples when scattering parameters are known. The common method of characterizing electromagnetic scattering properties involves identifying impedance (z) and refractive index (n). ε and μ are defined as ε = n/z and μ = nz. These are complex functions that satisfy causality requirements. For passive materials, Re(z) and Im(n) must be positive. The transmission coefficient for a 1-D slab is related to n and z. The reflection coefficient is also related to z and n. These equations can be inverted to find n and z as functions of t' and r. The expressions for n and z are complex and have multiple branches, leading to ambiguities. These ambiguities are resolved using additional knowledge about the material, such as the requirement that Re(z) > 0 for passive materials. The paper demonstrates the validity of assigning bulk ε and μ values to non-continuous metamaterials using simulation data from the transfer matrix method (TMM) on three types of structures: wires, SRRs, and a combination of both. The results show that the recovered ε and μ are consistent with the expected forms, with SRRs producing negative μ and wires producing negative ε. The combination of SRRs and wires results in both ε and μ being negative in a frequency range. The analysis also shows that the refractive index is negative in this frequency range, consistent with Veselago's theoretical prediction. The method is shown to be applicable to experimental characterization of metamaterial samples.This paper presents a method to determine the effective permittivity (ε) and permeability (μ) of electromagnetic metamaterials from reflection and transmission coefficients. The analysis is performed on structures composed of periodic arrangements of wires, split ring resonators (SRRs), and combinations of both. The recovered frequency-dependent ε and μ are consistent with analytic expressions predicted by effective medium arguments. A wire medium exhibits a frequency region where the real part of ε is negative, while SRRs produce a frequency region where the real part of μ is negative. In the combined structure, at frequencies where both ε and μ have negative real parts, the real part of the refractive index is also negative. The method involves using transmission and reflection coefficients (S-parameters) calculated for a wave incident on a finite slab of metamaterial. The scattering data is inverted to determine the refractive index (n) and impedance (z), from which self-consistent values for ε and μ are obtained. The technique is applicable to experimental characterization of metamaterial samples when scattering parameters are known. The common method of characterizing electromagnetic scattering properties involves identifying impedance (z) and refractive index (n). ε and μ are defined as ε = n/z and μ = nz. These are complex functions that satisfy causality requirements. For passive materials, Re(z) and Im(n) must be positive. The transmission coefficient for a 1-D slab is related to n and z. The reflection coefficient is also related to z and n. These equations can be inverted to find n and z as functions of t' and r. The expressions for n and z are complex and have multiple branches, leading to ambiguities. These ambiguities are resolved using additional knowledge about the material, such as the requirement that Re(z) > 0 for passive materials. The paper demonstrates the validity of assigning bulk ε and μ values to non-continuous metamaterials using simulation data from the transfer matrix method (TMM) on three types of structures: wires, SRRs, and a combination of both. The results show that the recovered ε and μ are consistent with the expected forms, with SRRs producing negative μ and wires producing negative ε. The combination of SRRs and wires results in both ε and μ being negative in a frequency range. The analysis also shows that the refractive index is negative in this frequency range, consistent with Veselago's theoretical prediction. The method is shown to be applicable to experimental characterization of metamaterial samples.