As of .NET 4.5, the SmtpClient class implements an async awaitable method, SendMailAsync. As a result, to send email asynchronously is as following:
public async Task SendEmail(string toEmailAddress, string emailSubject, string emailMessage)
{
var message = new MailMessage();
message.To.Add(toEmailAddress);
message.Subject = emailSubject;
message.Body = emailMessage;
using (var smtpClient = new SmtpClient())
{
await smtpClient.SendMailAsync(message);
}
}