Lo que tienes funcionará una vez que añadas

Private Const SYNCHRONIZE = &H100000

Que su falta. (Lo que significa 0 se pasa como el derecho de acceso a OpenProcess que no es válido)

Hacer Option Explicit la línea superior de todos sus módulos habría generado un error en este caso

El método WScript.Shell del objeto .Run() como se demuestra en La respuesta útil de Jean-François Corbett es la elección correcta si sabe que el comando que invoca terminará en el marco de tiempo esperado.

A continuación se SyncShell(), una alternativa que permite especificar un tiempo de espera , inspirado en el gran ShellAndWait() ejecución. (Este último es un poco pesado y, a veces, es preferible una alternativa más delgada.)

' Windows API function declarations.
Private Declare Function OpenProcess Lib "kernel32.dll" (ByVal dwDesiredAccessas As Long, ByVal bInheritHandle As Long, ByVal dwProcId As Long) As Long
Private Declare Function CloseHandle Lib "kernel32.dll" (ByVal hObject As Long) As Long
Private Declare Function WaitForSingleObject Lib "kernel32.dll" (ByVal hHandle As Long, ByVal dwMilliseconds As Long) As Long
Private Declare Function GetExitCodeProcess Lib "kernel32.dll" (ByVal hProcess As Long, ByRef lpExitCodeOut As Long) As Integer

' Synchronously executes the specified command and returns its exit code.
' Waits indefinitely for the command to finish, unless you pass a 
' timeout value in seconds for `timeoutInSecs`.
Private Function SyncShell(ByVal cmd As String, _
                           Optional ByVal windowStyle As VbAppWinStyle = vbMinimizedFocus, _
                           Optional ByVal timeoutInSecs As Double = -1) As Long

    Dim pid As Long ' PID (process ID) as returned by Shell().
    Dim h As Long ' Process handle
    Dim sts As Long ' WinAPI return value
    Dim timeoutMs As Long ' WINAPI timeout value
    Dim exitCode As Long

    ' Invoke the command (invariably asynchronously) and store the PID returned.
    ' Note that this invocation may raise an error.
    pid = Shell(cmd, windowStyle)

    ' Translate the PIP into a process *handle* with the
    ' SYNCHRONIZE and PROCESS_QUERY_LIMITED_INFORMATION access rights,
    ' so we can wait for the process to terminate and query its exit code.
    ' &H100000 == SYNCHRONIZE, &H1000 == PROCESS_QUERY_LIMITED_INFORMATION
    h = OpenProcess(&H100000 Or &H1000, 0, pid)
    If h = 0 Then
        Err.Raise vbObjectError + 1024, , _
          "Failed to obtain process handle for process with ID " & pid & "."
    End If

    ' Now wait for the process to terminate.
    If timeoutInSecs = -1 Then
        timeoutMs = &HFFFF ' INFINITE
    Else
        timeoutMs = timeoutInSecs * 1000
    End If
    sts = WaitForSingleObject(h, timeoutMs)
    If sts <> 0 Then
        Err.Raise vbObjectError + 1025, , _
         "Waiting for process with ID " & pid & _
         " to terminate timed out, or an unexpected error occurred."
    End If

    ' Obtain the process's exit code.
    sts = GetExitCodeProcess(h, exitCode) ' Return value is a BOOL: 1 for true, 0 for false
    If sts <> 1 Then
        Err.Raise vbObjectError + 1026, , _
          "Failed to obtain exit code for process ID " & pid & "."
    End If

    CloseHandle h

    ' Return the exit code.
    SyncShell = exitCode

End Function

' Example
Sub Main()

    Dim cmd As String
    Dim exitCode As Long

    cmd = "Notepad"

    ' Synchronously invoke the command and wait
    ' at most 5 seconds for it to terminate.
    exitCode = SyncShell(cmd, vbNormalFocus, 5)

    MsgBox "'" & cmd & "' finished with exit code " & exitCode & ".", vbInformation


End Sub

Shell-y-Espera en VBA _{^{(Edición compacta)}}

Sub ShellAndWait(pathFile As String)
    With CreateObject("WScript.Shell")
        .Run pathFile, 1, True
    End With
End Sub

Ejemplo de uso:

Sub demo_Wait()
    ShellAndWait ("notepad.exe")
    Beep 'this won't run until Notepad window is closed
    MsgBox "Done!"
End Sub

Adaptado de (y más opciones en) Sitio de Chip Pearson.

Llegaría a esto usando la función Timer. Averiguar aproximadamente cuánto tiempo le gustaría que la macro para pausar mientras el .exe hace lo suyo, y luego cambia el ' 10 ' en la línea comentada a cualquier hora (en segundos) que quieras.

Strt = Timer
Shell (ThisWorkbook.Path & "\ProcessData.exe")  
Do While Timer < Strt + 10     'This line loops the code for 10 seconds
Loop 
UserForm2.Hide 

'Additional lines to set formatting

Esto debería hacer el truco, hágamelo saber si no.