How can I restart a windows service programmatically in .NET

Take a look at the ServiceController class.

To perform the operation that needs to be done when the service is restarted, I guess you should do that in the Service yourself (if it is your own service).
If you do not have access to the source of the service, then perhaps you can use the WaitForStatus method of the ServiceController.

An example using by ServiceController Class

private void RestartWindowsService(string serviceName)
{
    ServiceController serviceController = new ServiceController(serviceName);
    try
    {
        if ((serviceController.Status.Equals(ServiceControllerStatus.Running)) || (serviceController.Status.Equals(ServiceControllerStatus.StartPending)))
        {
            serviceController.Stop();
        }
        serviceController.WaitForStatus(ServiceControllerStatus.Stopped);
        serviceController.Start();
        serviceController.WaitForStatus(ServiceControllerStatus.Running);
    }
    catch
    {
        ShowMsg(AppTexts.Information, AppTexts.SystematicError, MessageBox.Icon.WARNING);
    }
}

This article uses the ServiceController class to write methods for Starting, Stopping, and Restarting Windows services; it might be worth taking a look at.

Snippet from the article (the "Restart Service" method):

public static void RestartService(string serviceName, int timeoutMilliseconds)
{
  ServiceController service = new ServiceController(serviceName);
  try
  {
    int millisec1 = Environment.TickCount;
    TimeSpan timeout = TimeSpan.FromMilliseconds(timeoutMilliseconds);

    service.Stop();
    service.WaitForStatus(ServiceControllerStatus.Stopped, timeout);

    // count the rest of the timeout
    int millisec2 = Environment.TickCount;
    timeout = TimeSpan.FromMilliseconds(timeoutMilliseconds - (millisec2-millisec1));

    service.Start();
    service.WaitForStatus(ServiceControllerStatus.Running, timeout);
  }
  catch
  {
    // ...
  }
}