Upon finding the allegations of such application to be true, or that such judge of probate has been delinquent with respect to the filing of any record or document relating to any estate required by law to be filed with the Commissioner of Revenue Services, such superior court or judge may issue an order in the nature of a peremptory mandamus requiring such judge of probate to comply with the provisions of the statutes in relation thereto, which provisions shall be particularly mentioned in such order, and shall render judgment against such judge of probate, with costs as in mandamus proceedings. Any judge of probate who fails to comply with any order issued by the authority of the provisions of this section shall be in contempt, and the court or judge issuing the same may punish him therefor as in mandamus proceedings. Any person aggrieved by any order issued on such application shall have the same right to review by the Supreme Court as in case of mandamus proceedings.