Final answer:
The High Court of Australia (HCA) or the U.S. Supreme Court can either uphold the constitutionality of a law, strike down parts or the entire law, defer the decision, or in rare cases, seek international arbitration.
Step-by-step explanation:
The High Court of Australia (HCA) or the U.S. Supreme Court's judgement on a constitutional challenge to a law can have varying outcomes. These outcomes may include upholding the constitutionality of the law, thereby allowing it to remain in force; striking down parts or all of the law if found unconstitutional; or deferring the decision to another time or body such as the parliament to decide on a law's validity. In some instances, cases may also be taken to an international legal body, such as the Judicial Committee of the Privy Council for a decision, but this is less common with supreme national courts like the HCA or the U.S. Supreme Court, which are typically the final arbiters of constitutional issues in their respective countries.
In the case of the U.S. Supreme Court, as exemplified by decisions such as National Federation of Independent Business v. Sebelius, the Court upheld the Patient Protection and Affordable Care Act (ACA) by a 5-4 margin, demonstrating its role in interpreting the constitutionality of laws. The principle guiding such decisions is that any legislative act that is repugnant to the constitution is void. Similarly, the Judicial Committee of the Privy Council ruled in favor of women's rights in a historic decision, showing that courts can have a profound impact on societal norms and rights.