We report a search for signatures of cosmic strings in the the Cosmic Microwave Background data from the Wilkinson Microwave Anisotropy Probe. We used a digital filter designed to search for individual cosmic strings and found no evidence for them in the WMAP CMB anisotropies to a level of $Delta T/T sim 0.29$ mK. This corresponds to an absence of cosmic strings with $ Gmu ga 1.07 times 10^{-5}$ for strings moving with velocity $v = c/sqrt{2}$. Unlike previous work, this limit does not depend on an assumed string abundance. We have searched the WMAP data for evidence of a cosmic string recently reported as the CSL-1 object, and found an ``edge with 2$sigma$ significance. However, if this edge is real and produced by a cosmic string, it would have to move at velocity $ga$ 0.94c. We also present preliminary limits on the CMB data that will be returned by the PLANCK satellite for comparison. With the available information on the PLANCK satellite, we calculated that it would be twice as sensitive to cosmic strings as WMAP.