The longitudinal and transverse beam coupling impedance of the first final TOTEM Roman Pot unit has been measured in the laboratory with the wire method. For the evaluation of transverse impedance the wire position has been kept constant, and the insertions of the RP were moved asymmetrically. With the original configuration of the RP, resonances with fairly high Q values were observed. In order to mitigate this problem, RF-absorbing ferrite plates were mounted in appropriate locations. As a result, all resonances were sufficiently damped to meet the stringent LHC beam coupling impedance requirements.