DECLARE
  l_computed_value NUMBER;
  l_errmsg         VARCHAR2(500);
BEGIN
  FOR cur_r IN (SELECT id, name FROM some_table)
  LOOP
    BEGIN
      l_computed_value := do_some_computing_here;
      INSERT INTO your_table (id, name, computed_value)
      VALUES
      (cur_r.id, cur_r.name, l_computed_value);
    EXCEPTION
      WHEN OTHERS THEN
        l_errmsg := SQLERRM;
        INSERT INTO err_log_table (id, err)
        VALUES
        (cur_r.id, l_errmsg);
    END;
  END LOOP;
END;

SQL> declare
  2    l_eno number;
  3  begin
  4    select empno into l_eno from emp;
  5  end;
  6  /
declare
*
ERROR at line 1:
ORA-01422: exact fetch returns more than requested number of rows
ORA-06512: at line 4


SQL>

SQL> declare
  2    l_eno number;
  3  begin
  4    select empno into l_eno from emp;
  5  exception
  6    when others then null;
  7  end;
  8  /

PL/SQL procedure successfully completed.