This paper analyzes the effect of a frequency estimator in a grid-forming (GFM) synchronization control on the stability and control performance. GFM control for power converters has been proposed as a promising solution to enhance the stability and resilience of electrical systems dominated by power electronics. However, no consensus has been reached on the control structure for this operation mode. Moreover, the interactions between different GFM schemes and frequency estimators are not completely defined in the literature. In this paper, the effect of adding a frequency estimator to the two main industry-class synchronization controls, i.e., droop and virtual synchronous machine (VSM), is studied. Additionally, different AC voltage measurement points, tuning, and structures of frequency estimator are considered. Two distinct analyses are performed to discuss the characteristics of different configurations① an analytical study on the control performance of different configurations, and ② a small-signal analysis to ensure system stability. Finally, the results are validated using dynamic simulations, followed by a discussion. This paper concludes that the droop should be avoided when applying a frequency estimator, and other structures such as the VSM are more desirable.