The key method is in the MVC source code: GetAntiForgeryTokenAndSetCookie
This creates an instance of an internal sealed class called AntiForgeryData.
The instance is serialised into a cookie "__RequestVerificationToken_" + a base 64 encoded version of the application path.
The same instance of AntiForgeryData is serialised into a hidden input.
The unique part of the AntiForgeryData is got with an RNGCryptoServiceProvider.GetBytes()
All of this could be spoofed in a WebForms page, the only messy bit is the serialisation of the hidden sealed class. Unfortunately the key method (GetAntiForgeryTokenAndSetCookie) relies on ViewContext.HttpContext.Request to get at the cookies, while the WebForm needs to use HttpContext.Current.Request instead.
Update
Not much testing and a lot of code, but I think I've cracked this with a little reflection. Where I've used reflection I've left the equivalent line commented out above:
using System;
using System.Reflection;
using System.Web;
using System.Web.Mvc;
/// <summary>Utility to provide MVC anti forgery tokens in WebForms pages</summary>
public class WebFormAntiForgery
{
    /// <summary>Create an anti forgery token in a WebForms page</summary>
    /// <returns>The HTML input and sets the cookie</returns>
    public static string AntiForgeryToken()
    {
        string formValue = GetAntiForgeryTokenAndSetCookie();
        // string fieldName = AntiForgeryData.GetAntiForgeryTokenName(null);
        var mvcAssembly = typeof(HtmlHelper).Assembly;
        var afdType = mvcAssembly.GetType("System.Web.Mvc.AntiForgeryData");
        string fieldName = Convert.ToString(afdType.InvokeMember(
            "GetAntiForgeryTokenName",
            BindingFlags.NonPublic | BindingFlags.Static | BindingFlags.InvokeMethod,
            null,
            null,
            new object[] { null }));
        TagBuilder builder = new TagBuilder("input");
        builder.Attributes["type"] = "hidden";
        builder.Attributes["name"] = fieldName;
        builder.Attributes["value"] = formValue;
        return builder.ToString(TagRenderMode.SelfClosing);
    }
    static string GetAntiForgeryTokenAndSetCookie()
    {
        var mvcAssembly = typeof(HtmlHelper).Assembly;
        var afdType = mvcAssembly.GetType("System.Web.Mvc.AntiForgeryData");
        // new AntiForgeryDataSerializer();
        var serializerType = mvcAssembly.GetType("System.Web.Mvc.AntiForgeryDataSerializer");
        var serializerCtor = serializerType.GetConstructor(new Type[0]);
        object serializer = serializerCtor.Invoke(new object[0]); 
        // string cookieName = AntiForgeryData.GetAntiForgeryTokenName(HttpContext.Current.Request.ApplicationPath);
        string cookieName = Convert.ToString(afdType.InvokeMember(
            "GetAntiForgeryTokenName",
            BindingFlags.NonPublic | BindingFlags.Static | BindingFlags.InvokeMethod,
            null,
            null,
            new object[] { HttpContext.Current.Request.ApplicationPath }));
        // AntiForgeryData cookieToken;
        object cookieToken;
        HttpCookie cookie = HttpContext.Current.Request.Cookies[cookieName];
        if (cookie != null)
        {
            // cookieToken = Serializer.Deserialize(cookie.Value);
            cookieToken = serializerType.InvokeMember("Deserialize", BindingFlags.InvokeMethod, null, serializer, new object[] { cookie.Value });
        }
        else
        {
            // cookieToken = AntiForgeryData.NewToken();
            cookieToken = afdType.InvokeMember(
                "NewToken",
                BindingFlags.Public | BindingFlags.Static | BindingFlags.InvokeMethod,
                null,
                null,
                new object[0]);
            // string cookieValue = Serializer.Serialize(cookieToken);
            string cookieValue = Convert.ToString(serializerType.InvokeMember("Serialize", BindingFlags.InvokeMethod, null, serializer, new object[] { cookieToken }));
            var newCookie = new HttpCookie(cookieName, cookieValue) { HttpOnly = true };
            HttpContext.Current.Response.Cookies.Set(newCookie);
        }
        // AntiForgeryData formToken = new AntiForgeryData(cookieToken)
        // {
        //     CreationDate = DateTime.Now,
        //     Salt = salt
        // };
        var ctor = afdType.GetConstructor(new Type[] { afdType });
        object formToken = ctor.Invoke(new object[] { cookieToken });
        afdType.InvokeMember("CreationDate", BindingFlags.SetProperty, null, formToken, new object[] { DateTime.Now });
        afdType.InvokeMember("Salt", BindingFlags.SetProperty, null, formToken, new object[] { null });
        // string formValue = Serializer.Serialize(formToken);
        string formValue = Convert.ToString(serializerType.InvokeMember("Serialize", BindingFlags.InvokeMethod, null, serializer, new object[] { formToken }));
        return formValue;
    }
}
Usage is then similar to MVC:
WebFormAntiForgery.AntiForgeryToken()
It creates the same cookie and the same HTML as the MVC methods.
I haven't bothered with the salt and domain methods, but they would be fairly easy to add in.