There is a way to skip the errors inside the code and go on with the loop anyway, hope it helps:
Sub new1()
Dim wsFunc As WorksheetFunction: Set wsFunc = Application.WorksheetFunction
Dim ws As Worksheet: Set ws = Sheets(1)
Dim rngLook As Range: Set rngLook = ws.Range("A:M")
currName = "Example"
On Error Resume Next ''if error, the code will go on anyway
cellNum = wsFunc.VLookup(currName, rngLook, 13, 0)
If Err.Number <> 0 Then
''error appeared
MsgBox "currName not found" ''optional, no need to do anything
End If
On Error GoTo 0 ''no error, coming back to default conditions
End Sub