Never easily deterred, Giuliani and company vowed to appeal the case to the 3rd US Circuit Court of Appeals, which is their right. But they’ve got a major uphill climb, given Brann’s unequivocal finding that they offered no evidence and no cognizable legal theory. And the Trump team cannot offer up new evidence now, before the 3rd Circuit. As a procedural matter, federal courts of appeals typically consider only the evidentiary record that was before the district court, and do not take into account newly discovered evidence (not that there’s any indication Giuliani and his team actually have discovered any such thing).
Beyond that, the Trump team takes a broad leap of faith that the Supreme Court will agree to hear their case. While losing parties in federal court generally can appeal as a matter of right to the court of appeals, nobody has a right to be heard by the US Supreme Court. The decision to hear a case — called “certiorari,” in the lingo — is entirely up to the court itself, requiring a vote of at least four of the nine justices. The court typically grants certiorari in less than 5% of the cases brought to it for consideration. And the court usually tries to avoid getting involved in politically charged cases.