Characteristic multipliers (CMs) describe the behavior, such as stability, of a dynamical system near a limit cycle. While existing methods are available to estimate CMs from time series measurements of the system's state, practical challenges such as measurement noise, limited time series length, and repeated CMs can substantially reduce their accuracy. This paper describes a number of simple-to-implement improvements to existing methods which can be combined into a new, superior method. Numerical validation studies demonstrate that the new method consistently provides more accurate CM estimates than existing methods in a variety of scenarios.