Try this.
Note that cancel does not usually throw an error but does set myValue to NULL so it would look like nothing happened. Checking the strPtr value will show that it was really cancelled.
Sub AutoSuperscript()
Dim Message As String
Dim Title As String
Dim Default As String
Dim txtRange As TextRange2
Dim txtrangeSS As TextRange2
Dim myValue As String
'The Input box works well
Message = "Insert your superscripted text"
Title = "Superscript Input"
Default = "1"
myValue = InputBox(Message, Title, Default)
'Handles if User cancels
'On Error GoTo UserCancels
'I don't thing your original method really works
If StrPtr(myValue) = False Then GoTo UserCancels
'Adding the text at the position of the cursor - usually the end of a word - works, but it is not set to superscript mode:
Set txtRange = ActiveWindow.Selection.TextRange2
Set txtrangeSS = txtRange.InsertAfter(myValue)
txtrangeSS.Font.Superscript = True
'turn OFF SS
CommandBars.ExecuteMso ("Superscript")
Exit Sub
UserCancels:
Msgbox "Cancelled"
End Sub