If it's on the same server:
$con = mysqli_connect( 'end.do.servidor', 'usuario', 'senha ' );
if( !$con ) die( 'Falha na conexao: '.mysqli_connect_error( $con ) );
$sql1 = 'INSERT INTO nomedobanco1.tabela1 (....)';
$sql2 = 'INSERT INTO nomedobanco2.tabela2 (....)';
if( mysqli_query( $con, $sql1 ) ) echo 'Inserção 1 OK' else die( mysqli_error( $con ) );
if( mysqli_query( $con, $sql2 ) ) echo 'Inserção 2 OK' else die( mysqli_error( $con ) );
If they are different servers:
$con1 = mysqli_connect( 'end.do.servidor1', 'usuario', 'senha ' );
$con2 = mysqli_connect( 'end.do.servidor2', 'usuario', 'senha ' );
if( !$con1 ) die( 'Falha na conexao 1: '.mysqli_connect_error( $con1 ) );
if( !$con2 ) die( 'Falha na conexao 2: '.mysqli_connect_error( $con2 ) );
$sql1 = 'INSERT INTO nomedobanco1.tabela1 (....)';
$sql2 = 'INSERT INTO nomedobanco2.tabela2 (....)';
if( mysqli_query( $con1, $sql1 ) ) echo 'Inserção 1 OK' else die( mysqli_error($con1 ) );
if( mysqli_query( $con2, $sql2 ) ) echo 'Inserção 2 OK' else die( mysqli_error($con2 ) );
For PDO, the logic is the same, just adapt the syntax.
If you are using a single connection, and an engine as InnoDB, you can use BEGIN TRANSACTION
before% 2 INSERT
if COMMIT
then to ensure that the transaction is only if all goes well in both inserts, avoiding that only one table is modified. If you are using two connections, you need to think of another solution to ensure consistency.