Yes - it’s called an oath
Or, if you do not want to take a religious oath, you can make an affirmation instead which is legally the same but cuts out the deity.
If the document that is sworn or affirmed is to be used in a court or tribunal it’s called an affidavit, if not, it’s called a statutory declaration. In NSW how they are made is detailed in the Oaths Act 1900. Swearing or affirming a knowingly false statement is a criminal offence.
Other laws detail when they are required, for example, photo generated vehicle penalty notices have a blank statutory declaration on the back so the owner can identify the person in control of the vehicle. They can also be called up in contracts- they are pretty standard in construction contracts where a contractor must make a statutory declaration that all employees wages, entitlements and insurances have been paid as a prerequisite to their own payment from the principal.