By law, they are supposed to provide storage for your weapon, but not all do. The Utah County Courthouse in Provo will not store your weapon, they will make you leave it in your car.
78A-2-203. Rules -- Right to make -- Limitation -- Security.
(1) Every court of record may make rules, not inconsistent with law, for its own government and the government of its officers; but such rules must neither impose any tax or charge upon any legal proceeding nor give any allowance to any officer for service.
(2) (a) The judicial council may provide, through the rules of judicial administration, for security in or about a courthouse or courtroom, or establish a secure area as prescribed in Section 76-8-311.1.
(b) (i) If the council establishes a secure area under Subsection (2)(a), it shall provide a secure firearms storage area on site so that persons with lawfully carried firearms may store them while they are in the secure area.
(ii) The entity operating the facility with the secure area shall be responsible for the firearms while they are stored in the storage area referred to in Subsection (2)(b)(i).
(iii) The entity may not charge a fee to individuals for storage of their firearms under Subsection (2)(b)(i).
(3) (a) Unless authorized by the rules of judicial administration, any person who knowingly or intentionally possesses a firearm, ammunition, or dangerous weapon within a secure area established by the judicial council under this section is guilty of a third degree felony.
(b) Any person is guilty of violating Section 76-10-306 who transports, possesses, distributes, or sells an explosive, chemical, or incendiary device, as defined by Section 76-10-306, within a secure area, established by the Judicial Council under this section.
76-8-311.1. Secure areas -- Items prohibited -- Penalty.
(1) In addition to the definitions in Section 76-10-501, as used in this section:
(a) "Correctional facility" has the same meaning as defined in Section 76-8-311.3.
(b) "Explosive" has the same meaning as defined for "explosive, chemical, or incendiary device" defined in Section 76-10-306.
(c) "Law enforcement facility" means a facility which is owned, leased, or operated by a law enforcement agency.
(d) "Mental health facility" has the same meaning as defined in Section 62A-15-602.
(e) (i) "Secure area" means any area into which certain persons are restricted from transporting any firearm, ammunition, dangerous weapon, or explosive.
(ii) A "secure area" may not include any area normally accessible to the public.
(2) (a) A person in charge of a correctional, law enforcement, or mental health facility may establish secure areas within the facility and may prohibit or control by rule any firearm, ammunition, dangerous weapon, or explosive.
(b) Subsections (2)(a), (3), (4), (5), and (6) apply to higher education secure area hearing rooms referred to in Subsections 53B-3-103(2)(a)(ii) and (b).
(3) At least one notice shall be prominently displayed at each entrance to an area in which a firearm, ammunition, dangerous weapon, or explosive is restricted.
(4) (a) Provisions shall be made to provide a secure weapons storage area so that persons entering the secure area may store their weapons prior to entering the secure area.
(b) The entity operating the facility shall be responsible for weapons while they are stored in the storage area.
(5) It is a defense to any prosecution under this section that the accused, in committing the act made criminal by this section, acted in conformity with the facility's rule or policy established pursuant to this section.
(6) (a) Any person who knowingly or intentionally transports into a secure area of a facility any firearm, ammunition, or dangerous weapon is guilty of a third degree felony.
(b) Any person violates Section 76-10-306 who knowingly or intentionally transports, possesses, distributes, or sells any explosive in a secure area of a facility.