I don't know if this is the way it should be done:

{
...
var client = new SmtpClient {Host = _smtpServer};
client.SendCompleted += SendCompletedCallback;
var userState = mailMessage;
client.SendAsync(mailMessage, userState);
...
}

private static void SendCompletedCallback(object sender, 
    AsyncCompletedEventArgs e)
{
    // Get the unique identifier for this asynchronous operation.
    var mailMessage= (MailMessage)e.UserState;

    if (e.Cancelled)
    {
        Log.Info(String.Format("[{0}] Send canceled.", mailMessage));
    }
    if (e.Error != null)
    {
        Log.Error(String.Format("[{0}] {1}", mailMessage, e.Error));
    }
    else
    {
        Log.Info("Message sent.");
    }
    mailMessage.Dispose();
}

Disposing the mailMessage after the client.SendAsync(...) throws an error. So I need to dispose it in the Callback handler.