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1. The judicial power of Uganda shall be exercised by the courts of judicature which shall consist of-
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d. such subordinate courts as Parliament may by law establish, including qadhis courts for marriage, divorce, inheritance of property and guardianship, as may be prescribed by Parliament.
… (Art. 129)

Uganda shall not adopt a State religion. (Art. 7)

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2. If any other law or any custom is inconsistent with any of the provisions of this Constitution, the Constitution shall prevail, and that other law or custom shall, to the extent of the inconsistency, be void. (Art. 2)

1. Subject to the provisions of this Constitution, the institution of traditional leader or cultural leader may exist in any area of Uganda in accordance with the culture, customs and traditions or wishes and aspirations of the people to whom it applies.
2. In any community, where the issue of traditional or cultural leader has not been resolved, the issue shall be resolved by the community concerned using a method prescribed by Parliament.
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4. The allegiance and privileges accorded to a traditional leader or a cultural leader by virtue of that office shall not be regarded as a discriminatory practice prohibited under article 21 of this Constitution; but any custom, practice, usage or tradition relating to a traditional leader or cultural leader which detracts from the rights of any person as guaranteed by this Constitution, shall be taken to be prohibited under that article.
5. For the avoidance of doubt, the institution of traditional leader or cultural leader existing immediately before the coming into force of this Constitution shall be taken to exist in accordance with the provisions of this Constitution.
6. For the purposes of this article, "traditional leader or cultural leader" means a king or similar traditional leader or cultural leader by whatever name called, who derives allegiance from the fact of birth or descent in accordance with the customs, traditions, usage or consent of the people led by that traditional or cultural leader. (Art. 246)

Cultural and customary values which are consistent with fundamental rights and freedoms, human dignity, democracy and with the Constitution may be developed and incorporated in aspects of Ugandan life.
The State shall-
a. promote and preserve those cultural values and practices which enhance the dignity and well-being of Ugandans;
… (National Objectives and Directive Principles of State Policy, XXIV)

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3. Land in Uganda shall be owned in accordance with the following land tenure systems-
a. customary;
b. freehold;
c. mailo; and
d. leasehold.
4. On the coming into force of this Constitution-
a. all Uganda citizens owning land under customary tenure may acquire certificates of ownership in a manner prescribed by Parliament; and
b. land under customary tenure may be converted to freehold land ownership by registration.
… (Art. 237)

1. The judicial power of Uganda shall be exercised by the courts of judicature which shall consist of-
…
d. such subordinate courts as Parliament may by law establish, including qadhis courts for marriage, divorce, inheritance of property and guardianship, as may be prescribed by Parliament.
… (Art. 129)

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5. Without prejudice to article 32 of this Constitution, women shall have the right to affirmative action for the purpose of redressing the imbalances created by history, tradition or custom. (Art. 33)

Where a traditional leader or cultural leader exists in a region the traditional or cultural leader shall-
a. be the titular head of the regional government;
b. be the titular head of the regional assembly and shall open, address and close the sessions of the regional assembly; and
c. enjoy the benefits, privileges and roles as provided for in article 246 of this Constitution and by Parliament and the regional assembly. (Fifth Schedule: Regional governments, Art. 8)

1. Notwithstanding anything in this Constitution, the State shall take affirmative action in favour of groups marginalised on the basis of gender, age, disability or any other reason created by history, tradition or custom, for the purpose of redressing imbalances which exist against them.
2. Laws, cultures, customs and traditions which are against the dignity, welfare or interest of women or any other marginalised group to which clause (1) relates or which undermine their status, are prohibited by this Constitution.
… (Art. 32)