Paste Special Values losing destination formatting

That should work.

Option Explicit

' basic recorded macro with S1.B3 and S2.A4 pre-selected
Sub Macro1()
'
' Macro1 Macro
'

'
Selection.Copy
Sheets("Sheet2").Select
Selection.PasteSpecial Paste:=xlPasteValues, Operation:=xlNone, SkipBlanks _
    :=False, Transpose:=False
Columns("A:A").EntireColumn.AutoFit
End Sub

' adapted macro to avoid selection
Sub sCopyPasteSpecial()

Sheets("Sheet1").Range("B4").Copy
With Sheets("Sheet2")
    With .Range("A4")
        .PasteSpecial _
            Paste:=xlPasteValues, _
            Operation:=xlNone, _
            SkipBlanks:=False, _
            Transpose:=False
    End With
    .Columns("A:A").EntireColumn.AutoFit
End With

End Sub

Suggest you post a sample workbook that demonstrates the problem.