[ecfisa]

Hola barakuda.

Te ejemplifico dos modos.

Usando un TString aparejado:

Código Delphi [-]
...
implementation

var
  TS: TStrings;

procedure TForm1.FormCreate(Sender: TObject);
begin
  TS:= TStringList.Create;
  while not ADOQuery.Eof do
  begin
    ComboBox1.Items.Add(ADOQuery.Fields[0].Text);
    TS.Add(ADOQuery.Fields[1].Text);
    ADOQuery.Next;
  end;
end;
....
procedure TForm1.ComboBox1Change(Sender: TObject);
begin
  Edit1.Text := TS[ComboBox1.ItemIndex];
end;
...
procedure TForm1.FormDestroy(Sender: TObject);
begin
  TS.Free;
end;

Mediante el método AddItem del ComboBox:

Código Delphi [-]
...
implementation

type
  TCadena = class
    Text: string;
  end;

procedure TForm1.FormCreate(Sender: TObject);
var
  cad: TCadena;
begin
  while not ADOQuery.Eof do
  begin
    cad := TCadena.Create;
    cad.Text := ADOQuery.Fields[1].Text;
    ComboBox1.AddItem(ADOQuery.Fields[0].Text, TObject(cad));
    ADOQuery.Next;
  end;
end;
...
procedure TForm1.ComboBox1Change(Sender: TObject);
begin
  Edit1.Text := TCadena(ComboBox1.Items.Objects[ComboBox1.ItemIndex]).Text;
end;
...
procedure TForm1.FormDestroy(Sender: TObject);
var
  i: Integer;
begin
  for i:= ComboBox1.Items.Count-1 downto 0 do
    ComboBox1.Items.Objects[i].Free;
end;

Saludos.