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 C \ell over project as our example . In the null hypothesis ( that cosmic strings make a zero contribution ) we find that C \ell over should limit the string tension \mu to G \mu < 0.12 \times 10 ^ { -6 } ( where G is the gravitational constant ) , above which it is likely that a detection would be possible .