Synchronous generators are widely utilized in microgrids with high penetration of distributed renewable energy resources for small scale power generation. An accurate model of a synchronous generator is key to effective planning and operation of a grid-tied microgrid as well as stabilizing the frequency and regulating the voltage in an islanded microgrid. In this paper, a new strategy, based on the sensitivity trajectory analysis, for modeling a synchronous generator, which influences the transients of a microgrid greatly, is proposed. This method partitions the model parameters into significant and less significant sets. It is shown that in microgrid modeling, only the significant parameters need to be identified, and the remaining parameters can be replaced by typical values as they do not influence the model outputs critically. Reduction of the estimated parameters allows for modeling other components using on-line measurements, increases the reliability of the identified parameters and generalization capability of the characterizing model. The performance of the proposed approach is demonstrated by modeling a 5.3 MVA synchronous generator utilized in the San Diego State University microgrid.