The discovery of more than 500 exoplanets during the past 15 years has enabled us to characterize the upper atmosphere structure of some exosolar gas giants and to compare observational and modelling results to the known planets in the Solar System. It is of great interest to understand if these exosolar "Hot Jupiters" share similar physical processes compared to the giant planets (Jupiter and Saturn) in the Solar System with regard to their magnetic dynamos and the corresponding expected magnetic field strengths. In this work we discuss how observations of stellar Lyman-alpha absorption by so-called Energetic Neutral Atoms (ENAs) around transiting exoplanets together with theoretical modelling efforts can be used as a tool for estimating magnetic obstacle sizes and the corresponding magnetic field strength. For demonstrating this method we model the production of stellar wind related planetary hydrogen and ENA populations around the exosolar gas giant HD 209458b and show how a detailed analysis of attenuation spectra obtained during transits can be used for the estimation of the planet's magnetic obstacle size and hence its dynamo field strength. Our study indicates that the magnetic field strength of HD 209458b which is able to balance the stellar wind plasma flow by a magnetic obstacle around the planet which can explain the observed Lyman-alpha line profiles observed before and during the transits by HST corresponds to a magnetic dipole moment which is about 40 percent of Jupiters value.Read less <