When someone asserts under oath, they make a statement that is sworn to be true and accurate. Similar phrases to assert under oath include testify under oath, swear under oath, declare under oath, and affirm under oath. All of these phrases are used in a legal setting, typically in a courtroom or during a deposition, to ensure that the person making the statement is telling the truth. Other related words that are often used in this context include: testify, take an oath, solemnly swear, and give evidence. These phrases and words are critical because they establish the truth and help to ensure that justice is served.