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The scattering problem of time-harmonic electromagnetic plane waves by an impedance and a dielectric ellipsoid is considered. A low-frequency formulation of the direct scattering problem using the Rayleigh approximation is described. Considering far-field data, an inverse electromagnetic scattering problem is formulated and studied. A finite number of measurements of the leading-order term of the electric far-field pattern in the low-frequency approximation leads to specify the semi-axes of the ellipsoid. The orientation of the ellipsoid is obtained by using the Euler angles. Corresponding results for the sphere, spheroid, needle, and disc can be obtained considering them as geometrically degenerate forms of the ellipsoid for suitable values of its geometrical parameters.