Is there any way to connect to a second (MySQL) database in a Kernel Base test?
I have figured it out. The setUp() method in my Kernel Base Test must look like that:

/**
 * {@inheritdoc}
 */
protected function setUp() {
    parent::setUp();

    $databases['second-database']['default'] = array(
        'database' =&gt; 'second-database',
        'username' =&gt; 'second-database',
        'password' =&gt; 'second-database',
        'prefix' =&gt; '',
        'host' =&gt; 'localhost',
        'port' =&gt; '3306',
        'namespace' =&gt; 'Drupal\\Core\\Database\\Driver\\mysql',
        'driver' =&gt; 'mysql',
    );
    Database::setMultipleConnectionInfo(
        $databases
    );
}