I don't know what you're doing wrong, mort, but here is a quick example using basically what you are doing, and it works just fine:

Code:
Option Explicit
Dim AppExcel As Excel.Application
Dim objWb As Excel.Workbook

Private Sub cboNames_Click()  'NOTICE-I used the CLICK EVENT, not the CHANGE EVENT IN THE ComboBox, cboNames
    txtEmployeeNumber.Text = objWb.Worksheets(1).Cells(cboNames.ListIndex + 1, 2) 'NOTICE THE .Text, not .Value (as stated by others above)  '''also NOTE: I only have one worksheet in my workbook, hence (1).
End Sub



Private Sub Form_Load()
    cboNames.AddItem ("John")
    cboNames.AddItem ("Sam")
    cboNames.AddItem ("Sammi")
    cboNames.AddItem ("Bill")
    cboNames.AddItem ("James")
    Set AppExcel = CreateObject("Excel.Application")
    Set objWb = AppExcel.Workbooks.Add
    Set objWb = GetObject(App.Path & "\testfile.xlsx")  
End Sub
My Excel file (textfile.xlsx) looks like this:
Column A Column B
John 1
Sam 2
Sammie 3
Bill 4
James 5