From Hans Herber, this goes in the userform module and will produce the userform without that "X" Close button on the title bar:
Option Explicit
Private Const GWL_STYLE = (-16)
Private Const WS_SYSMENU = &H80000
Private Declare Function _
FindWindow Lib "User32" Alias "FindWindowA" ( _
ByVal lpClassName As String, _
ByVal lpWindowName As String) As Long
Private Declare Function _
GetWindowLong Lib "User32" Alias "GetWindowLongA" ( _
ByVal hWnd As Long, ByVal nIndex As Long) As Long
Private Declare Function _
SetWindowLong Lib "User32" Alias "SetWindowLongA" ( _
ByVal hWnd As Long, ByVal nIndex As Long, _
ByVal dwNewLong As Long) As Long
Private Declare Function _
DrawMenuBar Lib "User32" (ByVal hWnd As Long) As Long
Private Sub UserForm_Initialize()
Dim xl_hwnd, lStyle
xl_hwnd = FindWindow(vbNullString, Me.Caption)
If xl_hwnd <> 0 Then
lStyle = GetWindowLong(xl_hwnd, GWL_STYLE)
lStyle = SetWindowLong(xl_hwnd, GWL_STYLE, lStyle And Not WS_SYSMENU)
DrawMenuBar xl_hwnd
End If
End Sub