Found that setting the secure property in Session_Start is sufficient, as recommended in MSDN blog "Securing Session ID: ASP/ASP.NET" with some augmentation.
protected void Session_Start(Object sender, EventArgs e)
{
SessionStateSection sessionState =
(SessionStateSection)ConfigurationManager.GetSection("system.web/sessionState");
string sidCookieName = sessionState.CookieName;
if (Request.Cookies[sidCookieName] != null)
{
HttpCookie sidCookie = Response.Cookies[sidCookieName];
sidCookie.Value = Session.SessionID;
sidCookie.HttpOnly = true;
sidCookie.Secure = true;
sidCookie.Path = "/";
}
}