What is the punishment for receiving a seruv from a Bais Din for litigating B'Arkoas (in non-Jewish courts) without a heter?
A search found the following on the consequences of a shtar siruv:
Resolved, that any person against whom there is an outstanding Shetar Siruv, issued by a Beit Din consisting of three Orthodox Rabbis, in regard to matters of issuance or receipt of a Get: 1. Shall not be permitted to occupy any elective or appointed position, or position as employee, within the Synagogue organization or within any of its affiliates. 2. Shall be excluded from membership in the Synagogue or in any of its affiliates. 3. Shall not be called to the Torah nor be given any other liturgical honor on any occasion.
Further, that such person who reside within our community: 4. Shall have his or her name announced on a regular monthly basis at the conclusion of Sabbath services. 5. Shall have his or her name published in the Synagogue bulletin with a call to the membership to limit their social and economic relations to such persons.
2) Rabbinical Court of Greater Cleveland Feb 2005. The named person is subject to the strictures of Yoreh Deah 334 (2).
A summoning beth din may issue a “seruv,” or a contempt order. A seruv is simply a public declaration by a beth din that someone was summoned to beth din but refused to meet their obligation under Jewish law to appear in front of the beth din. Sometimes, Jewish communities or synagogues impose sanctions on such people, such as not giving them aliyos (being called up to the reading of the Torah) or refraining from social interaction, to pressure the person to meet their obligation. The beth din is not necessarily involved at that point – the community or synagogue decides what measures are appropriate.
I did not find how these were applied practically.
Are you asking how G-d punishes it? I don't know.
As far as what we can do today, today's batei din don't have the power of corporeal punishment. (Israel is a bit more complicated, let's assume we're talking elsewhere.) Depending on the language of the seruv, the rabbis could call on the Jewish community to shun the individual; deny him any honors in synagogue; or potentially even bar his entrance to synagogue altogether. Shulchan Aruch discusses different levels of bans, some of which would mean the individual can't even count for a minyan. Rabbenu Tam is famous for describing an agreement that no one in the Jewish community would do business with someone found in contempt; my understanding is this is rarely used today (but I heard Rabbi Hershel Schachter state it might be necessary to bring it back).
In short, it can vary, and it only works based on how people in the local community agree to abide by it. If the fellow under contempt walks away from the community altogether, well we live in a liberal society and there's little we can do. (Though we could still assemble peaceful protests on public land outside the guy's house, for instance.)