Make a custom .NET Exception serializable

More specifically, when the exception contains custom objects which may or may not themselves be serializable.

Take this example:

public class MyException : Exception
{
    private readonly string resourceName;
    private readonly IList<string> validationErrors;

    public MyException(string resourceName, IList<string> validationErrors)
    {
        this.resourceName = resourceName;
        this.validationErrors = validationErrors;
    }

    public string ResourceName
    {
        get { return this.resourceName; }
    }
    
    public IList<string> ValidationErrors
    {
        get { return this.validationErrors; }
    }
}

If this Exception is serialized and de-serialized, the two custom properties (ResourceName and ValidationErrors) will not be preserved. The properties will return null.

How can I implement serialization for custom exceptions?