This paper considers speed estimation for contactless electromagnetic (EM) encoder system with a moving read-head and spatially periodic placed reflectors. We first introduce a new signal model to capture reflected signals from these spatially periodic placed reflectors. Then an instantaneous phase-based speed estimator is proposed by using the phase unwrapping technique followed by a nonlinear least square method for motion-related parameters. The proposed speed estimator is verified by 1) Monte-Carlo simulations to confirm its statistical efficiency as the numerical mean squared errors approach to corresponding Cramér-Rao bounds and 2) a semi-analytical dataset by accounting for real system specificaltions such as the antenna beampattern, 3-dB beamwidth, and noise.