Use the PostMessage api function.

Code:
Declare Function FindWindow Lib "user32" Alias _
"FindWindowA" (ByVal lpClassName As String, _
ByVal lpWindowName As String) As Long                    
Declare Function PostMessage Lib "user32" Alias _
"PostMessageA" (ByVal hwnd As Long, ByVal wMsg As Long, _
ByVal wParam As Long, lParam As Any) As Long                    
Public Const WM_CLOSE = &H10        

Dim winHwnd As Long
Dim RetVal As Long
winHwnd = FindWindow(vbNullString, "Calculator")
Debug.Print winHwnd
If winHwnd <> 0 Then
    RetVal = PostMessage(winHwnd, WM_CLOSE, 0&, 0&)
    If RetVal = 0 Then
        MsgBox "Error posting message."
    End If
Else
    MsgBox "The Calculator is not open."
End If
Another way would be to use the CloseHandle api function (this way, you can close a program by knowing it's file path).

Code:
Declare Function ProcessFirst Lib "kernel32" Alias "Process32First" (ByVal hSnapshot As Long, uProcess As PROCESSENTRY32) As Long
Declare Function ProcessNext Lib "kernel32" Alias "Process32Next" (ByVal hSnapshot As Long, uProcess As PROCESSENTRY32) As Long
Declare Function CreateToolhelpSnapshot Lib "kernel32" Alias "CreateToolhelp32Snapshot" (ByVal lFlags As Long, lProcessID As Long) As Long
Declare Function CloseHandle Lib "kernel32" (ByVal hObject As Long) As Long

Type PROCESSENTRY32
    dwSize As Long
    cntUsage As Long
    th32ProcessID As Long
    th32DefaultHeapID As Long
    th32ModuleID As Long
    cntThreads As Long
    th32ParentProcessID As Long
    pcPriClassBase As Long
    dwFlags As Long
    szexeFile As String * MAX_PATH
    End Type


Public Function KillApp(myName As String) As Boolean
    Const PROCESS_ALL_ACCESS = 0
    Dim uProcess As PROCESSENTRY32
    Dim rProcessFound As Long
    Dim hSnapshot As Long
    Dim szExename As String
    Dim exitCode As Long
    Dim myProcess As Long
    Dim AppKill As Boolean
    Dim appCount As Integer
    Dim i As Integer
    On Local Error GoTo Finish
    appCount = 0
    
    Const TH32CS_SNAPPROCESS As Long = 2&
    
    uProcess.dwSize = Len(uProcess)
    hSnapshot = CreateToolhelpSnapshot(TH32CS_SNAPPROCESS, 0&)
    rProcessFound = ProcessFirst(hSnapshot, uProcess)
    
    Do While rProcessFound
        i = InStr(1, uProcess.szexeFile, Chr(0))
        szExename = LCase$(Left$(uProcess.szexeFile, i - 1))
        If Right$(szExename, Len(myName)) = LCase$(myName) Then
            KillApp = True
            appCount = appCount + 1
            myProcess = OpenProcess(PROCESS_ALL_ACCESS, False, uProcess.th32ProcessID)
            AppKill = TerminateProcess(myProcess, exitCode)
            Call CloseHandle(myProcess)
        End If
        rProcessFound = ProcessNext(hSnapshot, uProcess)
    Loop

    Call CloseHandle(hSnapshot)
Finish:
End Function

Usage:

Call KillApp("C:\Windows\Calc.exe")