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.