I am trying to place a border around some cells I pasted using a macro.
My problem is that I don't know the location of the pasted cells
because I am pasting to the next empty row below other data. See below:

Set rng = Sheets("files").Cells(Rows.count, 2).End(xlUp)(2).Offset(2,
0)

range("C3:D5").Copy
rng.PasteSpecial xlFormats
rng.PasteSpecial xlValues

Is there a way I can place a border around the pasted cells with just
the info from this code?

Nevermind, I got it. Just had to activate the sheet:

Sheets("files").Activate
Selection.Borders(xlEdgeTop).LineStyle = xlDouble