Methods for classifying objects based on spatially sampled electromagnetic induction data taken in the time or frequency domain are developed and analyzed. To deal with nuisance parameters associated with the position of the object relative to the sensor as well as the object orientation, a computationally tractable physical model explicit in these unknowns is developed. The model is also parameterized by a collection of decay constants (or equivalently Laplace-plane poles) whose values in theory are independent of object position and orientation. These poles are used as features for classification. The overall algorithm consists of two stages. First, we estimate the values of the unknown parameters and then we do classification. Classification is done by comparing either the raw data or some low-dimensional collection of features extracted from the data to entries in a library. The library can be constructed using either simulated or calibration data. A maximum likelihood method is developed and analyzed for the problem of joint pole, location, and orientation parameter determination. Here we examine and compare two classification schemes. The first classification method is based on data residuals generated from estimated signal parameters. This scheme performs well in low SNR cases. The second is based on estimated pole values themselves, which performs well in high SNR cases. We validate our methods on both simulated and field data taken from frequency and time domain sensors.