The nucleon strange vector and isoscalar electromagnetic form factors are studied using a spectral decomposition. The K\bar{K} contribution to the electric and magnetic radii as well as the magnetic moment is evaluated to all orders in the strong interaction using an analytic continuation of experimental KN scattering amplitudes and bounds from unitarity. The relationship between non-resonant and resonant K\bar{K} contributions to the form factors is demonstrated, and values for the vector and tensor \phi N\bar{N} couplings are derived. The K\bar{K} spectral functions are used to evaluate the credibility of model calculations for the strange quark vector current form factors.