The effective rate is an important performance metric of real-time applications in next generation wireless networks. In this paper, we present an analysis of the effective rate of multiple-input single-output (MISO) systems over α-μ fading channels under a maximum delay constraint. More specifically, novel and highly accurate closed-form approximate expressions of the effective rate are derived for such systems assuming the generalized α-μ channel model. In order to examine the impact of system and channel parameters on the effective rate, we also derive closed-form expressions of the effective rate in asymptotically high and low signal-to-noise ratio (SNR) regimes. Furthermore, connections between our derived results and existing results from the literature are revealed for the sake of completeness. Our results demonstrate that the effective rate is a monotonically increasing function of channel fading parameters α and μ, as well as the number of transmit antennas, while it decreases to zero when the delay constraint becomes stringent.