We present the first calculation of the possible (local) cosmic string contribution to the cosmic microwave background polarization spectra from simulations of a string network (rather than a stochastic collection of unconnected string segments). We use field theory simulations of the Abelian Higgs model to represent local U(1) strings, including their radiative decay and microphysics. Relative to previous estimates, our calculations show a shift in power to larger angular scales, making the chance of a future cosmic string detection from the B-mode polarization slightly greater. We explore a future ground-based polarization detector, taking the CLOVER project as our example. In the null hypothesis (that cosmic strings make a zero contribution) we find that CLOVER should limit the string tension mu to Gmu<0.12e-6 (where G is the gravitational constant), above which it is likely that a detection would be possible.