I have a cer file called "Test.cer". I am doing the following in my code..

Certificate mycer = null;
mycer = Certificate.CreateFromCerFile(@"Test.cer");

SecurityOptions sc = new SecurityOptions(SecureProtocol.Tls1,mycer,ConnectionEnd.Client);

m_Socket = new SecureSocket(AddressFamily.InterNetwork,SocketType.Stream,ProtocolType.Tcp,sc);

....
....

Now, the error I am getting when I run the above console app is "If a certificate is specified, it must have a private key."

Any ideas will be appreciated.

Certificates are not always associated with a private key. Keep in mind that a certificate only says something about a public key.

CER files typically do not contain the private key that is associated with a certificate. Try using PFX files instead.