In this paper the concept of ship propulsion system “fingerprinting” is explored as an alternative for data driven models that require extensive measured datasets collected over long periods of ship operation. As a first exploratory step a model of a ship in bollard pull conditions is linearised and its transfer functions are determined. Subsequently limited experimental data, involving sinusoidal excitation of the system input at a wide range of frequencies, is used to determine the system parameters. The resulting parameter estimates compare well against previously determined values. Although the developed ideas are far from ready to be used on full scale, the authors believe that the approach is promising enough to be developed further towards full scale application.