We present a search for a new narrow, spin-1, high mass resonance decaying to μ+μ−+X, using a matrix-element-based likelihood and a simultaneous measurement of the resonance mass and production rate. In data with 4.6  fb−1 of integrated luminosity collected by the CDF detector in pp collisions at s√=1960  GeV, the most likely signal cross section is consistent with zero at 16% confidence level. We therefore do not observe evidence for a high mass resonance and place limits on models predicting spin-1 resonances, including M>1071  GeV/c2 at 95% confidence level for a Z′ boson with the same couplings to fermions as the Z boson.