For a User Run

strComputer = "."
strUser = "User"
strDomain = "domain"
Set objWMIService = GetObject("winmgmts:\\" & strComputer & "\root\cimv2")

Set objAccount = objWMIService.Get _
    ("Win32_UserAccount.Name='" & strUser &"',Domain='''& strDomain &"'")
Wscript.Echo objAccount.SID

For a Group Use

strComputer = "."
strGroup = "GROUPNAME"
strDomain = "DOMAIN"
Set objWMIService = GetObject("winmgmts:\\" & strComputer & "\root\cimv2")
Set objAccount = objWMIService.Get("Win32_Group.Name='" & strGroup &"',Domain='"& strDomain &"'")
Wscript.Echo objAccount.SID