Frequency response measurement on a transformer is a low voltage, off-line exercise. So, it virtually permits determination of any network/system function, by imposing any desired terminal condition for the nontested windings. The terminal conditions employed have significant influence on the achievable fault detection ability, and maximizing this ability should obviously be one of the main aims of frequency response measurements. Simply stated, this requirement translates to the ability to identify/measure as many natural frequencies as possible. However, there is a practical limitation that not all network/system functions can exhibit all natural frequencies. Hence, it is necessary to determine the most appropriate combination of terminal connection and system function for achieving this objective. Considering a two-winding transformer representation, system functions for different terminal conditions were computed. Depending on number of natural frequencies distinguishable in the amplitude frequency response of a system function, each measuring condition was ranked. Thus, it led to identification of the best configuration. Later, these findings were verified on an actual transformer. Performance of best configuration was compared with currently employed low-voltage impulse (LVI) test (used during short-circuit testing of transformers) and sweep frequency response measurement test conditions, and found to be better. In conclusion, it is believed that after adequate field verifications, the identified configuration can be declared as the preferred way of making frequency response measurements on transformers.