you could try the following but it relies upon cells always being populated
rngOrigin.End(xlDown).End(xlRight)
or you could use the CurrentRegion and count the rows and columns and use Offset
Alternatively, you could use this construct which works even with ranges based on entire rows or entire columns.
Sub Test()
Dim rngOrigin As Excel.Range
Set rngOrigin = Range("$A$1:$D$6")
Dim rngLast As Excel.Range
Set rngLast = rngOrigin.Cells(rngOrigin.Cells.Count)
Debug.Print rngLast.Address
End Sub
Finally, for ranges with multiple areas you'll have to script against a range's Areas collection ...
Sub Test()
Dim rngOrigin As Excel.Range
Set rngOrigin = Range("$A$1:$D$6,$F$1:$G$6")
Debug.Print rngOrigin.Areas(1).Cells(rngOrigin.Areas(1).Cells.Count).Address
Debug.Print rngOrigin.Areas(2).Cells(rngOrigin.Areas(2).Cells.Count).Address
End Sub