MyIEBitmap.CopyToClipboard(True, True);

procedure SetBuffer(Format: Word; const Buffer; Size: Integer);
var
  DataPtr: Pointer;
  Data: THandle;
begin
  Data := GlobalAlloc(GMEM_MOVEABLE+GMEM_DDESHARE, Size);
  try
    DataPtr := GlobalLock(Data);
    try
      Move(Buffer, DataPtr^, Size);
      Win32Check(SetClipboardData(Format, Data) <> 0);
    finally
      GlobalUnlock(Data);
    end;
  except
    GlobalFree(Data);
    raise;
  end;
end;

Clipboard.Open;
try
  MyIEBitmap.CopyToClipboard(True, True);
  const ThisID: string = 'UniqueID';
  SetBuffer(CF_UNICODETEXT, Text[1], ByteLength(ThisID));
finally
  Clipboard.Close;
end;

Clipboard.Open;
try
  Clipboard.Assign(MyIEBitmap.VclBitmap);
  Clipboard.AsText := 'MyUniqueID';
finally
  Clipboard.Close;
end;