Glenn,

This code should do it. But I have to say that seems a dumb policy to me, I
wouldn't be surprised if people are deliberately 4 minutes late because of
it, and if they are 6 minutes late, they would wait until they are 19
minutes late to not be taken advantage of.

Private Sub Worksheet_Change(ByVal Target As Range)

   On Error GoTo ws_exit:
   Application.EnableEvents = False
   If Not Intersect(Target, Me.Range("A1:A100")) Is Nothing Then
       With Target
           If .Value - Int(.Value * 24 * 4) / 24 / 4 > (1 / 24 / 12) Then
               .Value = Int(.Value * 24 * 4) / 24 / 4 + (1 / 24 / 4)
           End If
       End With
   End If

ws_exit:
   Application.EnableEvents = True
End Sub

'This is worksheet event code, which means that it needs to be
'placed in the appropriate worksheet code module, not a standard
'code module. To do this, right-click on the sheet tab, select
'the View Code option from the menu, and paste the code in.