Rule 62.1 allows a District Court (a trial level federal court) to indicate to a Circuit Court (an appellate level federal court) that it would  reconsider its previous ruling if the Circuit Court would return the case back to the District Court.

Consider the following situation:

A party receives an unfavorable ruling in a District Court.  While an appeal is pending before the Circuit Court, the party realizes that it did not provide the District Court with an important piece of evidence.  Unfortunately,  it is too late for the District Court to grant a motion for reconsideration.  

Rule 62.1 enables that party to ask the District Court to indicate that it believes a motion for reconsideration has merit.    If the District Court agrees and states that the motion has merit, then the party may ask the Circuit Court to remand (return) the case back to the District Court.  

Once the District Court has the case back from the Circuit Court, it may grant the motion for reconsideration.