No there doesn’t. The Senate could essentially dismiss the matter with no trial at all, and no avenue of appeal, either.
The Senate doesn't have the authority under the Constitution to stop an impeachment trial. Their only role in the matter is to vote guilty or not guilty on the Articles of Impeachment after a trial. The person with the authority to dismiss the Articles without a trial is the Chief Justice of the Supreme Court who would be the presiding judge in an impeachment trial.