This is what I have come up with.
Since you didn't provided any sample data I have used the following:
a b 23-12-2010 23-12-2010
aa bb 24-12-2010
aaa bbb 23-12-2010
In which column A is first name, Column B is Last name, Column C is reminder date, D1 is today's date using formula: =TODAY().
Open VB and paste the following code under ThisWorkbook:
Private Sub Workbook_BeforeClose(Cancel As Boolean)
Set MR = Range("C1:C3")
For Each cell In MR
If cell.Value = Range("D1").Value Then MsgBox (cell.Offset(0, -2).Value & " " & cell.Offset(0, -1))
When you close your workbook now, you will get message box after message box each with first and last name of the people you need to e-mail.