So far a criminal justice is concerned, there is no requirement for any government court, Jewish or non-Jewish, to conform to the standards of a sanhedrin. This was only for a time when Am Yisrael are all tzaddikim and crime is extremely rare (Maharal Chiddushei Aggadot Makkot 7a). In other times it is necessary for the government to establish its own standards in order to prevent anarchy (Ran Derasha 11 and Igerot Moshe Choshen Mishpat 2:68). This is especially true of murderers, who may be executed even where the Tora exempts them from punishment by the bet din (Rambam Hilchot Rotzeach 2:4 and Hilchot Melachim 9:14).Thus David HaMelech ordered the ger Amaleki executed on his confession alone (Shmuel Bet 1:14).This is not revenge but both for the protection of society (Rabban Shimon ben Gamliel’s response to Rabbi Akiva and Rabbi Tarfon, Mishna Makkot 2:10) and to enable the murderer to atone (by being executed).
Obviously, great care must be taken not to execute an innocent person but in a case where there is no doubt or virtually no doubt it is definitely in order.
So far as serving on a jury is concerned, in many cases they only rule on guilt or innocence and the judge decides the sentence.In any case, in view of the above I would think that it is davka a mitzva to serve on a jury in a criminal case.