Courthouses in Newcastle, Wyoming, the US. Courthouses locations in Newcastle, Wyoming. Find the nearest courthouses locations, near you. All types of business services Accounting ATM Bank Courthouse Finance Insurance Lawyer Real estate School All courthouses in Newcastle District Court Judge Courthouse +1 307-746-4681 1 West Main Street, Newcastle, Wyoming 82701 Write a review Phone Directions Weston County Circuit Court Courthouse +1 307-746-3547 6 West Warwick Street, Newcastle, Wyoming 82701 Write a review Phone Website Directions