1. Required to access the Classic ASP session state variable.
2. Required to share session state between multiple web applications.

Step #1:
The following code is in a page called AspSession.asp in the classic asp application.

<% 
'------------------------------------------------------------------------------
if Session.Contents.Count = 0 then
    response.Write "Session.Contents.Count = 0"
    response.End
end if

'------------------------------------------------------------------------------
Dim values,remoteAddr,localAddr

remoteAddr = Request.ServerVariables("REMOTE_ADDR")
localAddr = Request.ServerVariables("LOCAL_ADDR")

'------------------------------------------------------------------------------
if remoteAddr = localAddr then
    strMode = Request.QueryString( "mode" )
    strName = Request.QueryString( "name" )

    if strMode = "get" then
        response.Write GetSessionVar( strName )
    elseif strMode = "getall" then
        response.Write GetAllSessionVars()
    elseif strMode = "set" then
        strValue = Request.QueryString( "value" )
        Session( strName ) = strValue
    end if
end if

'------------------------------------------------------------------------------
function GetAllSessionVars()
    dim sessionVars

    sessionVars = ""
    for each key in Session.Contents
        sessionVars = sessionVars & "{" & GetSessionVar( key ) & "}"
    next

    GetAllSessionVars = sessionVars
end function

'------------------------------------------------------------------------------
' returns a single session variable
function GetSessionVar( byval name )

    If IsArray(Session.Contents(name)) Then
        GetSessionVar = GetArrayVar
    ElseIf IsObject( Session.Contents(name) ) Then
        GetSessionVar = GetObjectDictionaryVar( name )
    Else
        GetSessionVar = name & "|" & Session.Contents(name)
    End If

end function

'------------------------------------------------------------------------------
' assumes this is an object/dictionary session variable.
function GetObjectDictionaryVar( byval name )
    dim values

    values = name & "[Object/Dictionary]"
    for each key in Session.Contents(name)
        values = values & key & ":" & Session.Contents(name)(key) & "|"
    next

    GetObjectDictionaryVar = values
end function

'------------------------------------------------------------------------------
' assumes this is an array session variable.
function GetArrayVar( byval name )
    dim values

    values = name & "[Array]"
    for each key in Session.Contents(name)
        values = values & key & ":" & Session.Contents(name)(key) & "|"
    next

    GetArrayVar = values
end function
%>

// Contains properties, etc for session state management. This class needs to be
// serializable so it can be saved in session state.
[Serializable]
public class SessionStateManager
{
    //-------------------------------------------------------------------------
    // This calls a web page in the classic asp application to get it's 
    // current session variables.
    public static object Get( string name )
    {
        HttpContext context = HttpContext.Current;
        if ( context == null )
            return string.Empty;

        string value = null;
        foreach ( string key in context.Request.Cookies.AllKeys )
        {
            HttpCookie cookie = context.Request.Cookies[key];
            if ( cookie != null )
            {
                if ( cookie.Name.StartsWith( "ASPSESSION" ) )
                {
                    System.Uri uri = context.Request.Url;
                    string url = string.Format( "{0}://{1}/appName/aspSession.asp?mode=get&name={2}",
                                                 uri.Scheme, uri.Host, name );
                    HttpWebRequest request = (HttpWebRequest)WebRequest.Create( url );
                    request.Headers.Add( "Cookie: " + cookie.Name + "=" + cookie.Value );
                    HttpWebResponse response = (HttpWebResponse)request.GetResponse();
                    Stream responseStream = response.GetResponseStream();
                    if ( responseStream != null )
                    {
                        System.Text.Encoding encode = System.Text.Encoding.GetEncoding( "utf-8" );
                        StreamReader readStream = new StreamReader( responseStream, encode );
                        value = readStream.ReadToEnd();
                        response.Close();
                        readStream.Close();

                        // if true then it is either the wrong cookie or an expired cookie
                        // and will eventually be removed by the system.
                        if ( value.Equals( "Session.Contents.Count = 0" ) )
                        {
                            value = null;
                            continue;
                        }

                        string[] item;
                        if ( value.StartsWith( name + "[Object/Dictionary]" ) )
                        {
                            value = value.Replace( name + "[Object/Dictionary]", "" );
                            Dictionary<string,string> dictionary = new Dictionary<string, string>();
                            string[] dictionaryItems = value.Split( '|' );
                            foreach ( string s in dictionaryItems )
                            {
                                item = s.Split( ':' );
                                if ( item.Length == 2 )
                                    dictionary.Add( item[0], item[1] );
                            }
                            return dictionary;
                        }

                        item = value.Split( '|' );
                        if ( item.Length == 2)
                            value = (item.Length == 2) ? item[1] : string.Empty;
                    }
                }
            }
        }
        return value;
    }

    //-------------------------------------------------------------------------
    //  Disclaimer: This method hasn't been tested.
    //  Use this to set a session variable in the classic asp application. 
    public static void Set( string name, object value )
    {
        HttpContext context = HttpContext.Current;
        String[] cookies = context.Request.Cookies.AllKeys;

        foreach ( string key in context.Request.Cookies.AllKeys )
        {
            HttpCookie cookie = context.Request.Cookies[key];
            if ( cookie != null && cookie.Name.StartsWith( "ASPSESSION" ) )
            {
                System.Uri uri = context.Request.Url;
                string url = string.Format( "{0}://{1}/appName/aspSession.asp?mode=set&name={2}&value={3}",
                                            uri.Scheme, uri.Host,
                                            context.Server.UrlEncode( name ),
                                            context.Server.UrlEncode( value.ToString() ) );
                HttpWebRequest request = (HttpWebRequest)WebRequest.Create( url );
                request.Headers.Add( "Cookie: " + cookie.Name + "=" + cookie.Value );
                HttpWebResponse response = (HttpWebResponse)request.GetResponse();
                Stream responseStream = response.GetResponseStream();
                break;
            }
        }
    }
}