Handling exceptions like API timeouts or malformed JSON in a Python script is crucial for maintaining its reliability. First, I would use a try-except block to catch these exceptions. For an API timeout, I would implement a retry mechanism using libraries like `requests` with a backoff strategy to prevent overwhelming the server. If the JSON is malformed, I would log the error for further analysis and skip processing that particular response to ensure the script continues running. Additionally, I would include logging throughout the script to monitor its performance and identify any recurring issues. This approach ensures the script remains robust and continues to function even when encountering errors.