Base64UrlExtensions as specified by rfc4648 ((https://tools.ietf.org/html/rfc4648#section-5)

Base64UrlExtensions

    public static class Base64UrlExtensions
    {
        /// <summary>
        /// Encodes string to base64url, as specified by rfc4648 (https://tools.ietf.org/html/rfc4648#section-5)
        /// </summary>
        /// <returns></returns>
        public static string ToBase64Url(this string str)
        {
            // TODO - adds reference to System.Web
            if (str == null)
                throw new ArgumentNullException("str");
            var customBase64 = HttpServerUtility.UrlTokenEncode(Encoding.UTF8.GetBytes(str));
            return customBase64.Length == 0 ? customBase64 : customBase64.Substring(0, customBase64.Length - 1);
        }

        public static string FromBase64Url(this string rfc4648)
        {
            if (rfc4648.Length%4 != 0)
                rfc4648 += (4 - rfc4648.Length%4);
            else
                rfc4648 += 0;

            return Encoding.UTF8.GetString(HttpServerUtility.UrlTokenDecode(rfc4648));
        }
    }

Base64UrlExtensionsTest

    [TestFixture]
    public class Base64UrlExtensionsTest
    {
        [TestCase("a", "YQ")] // basic string handling
        [TestCase("", "")] // empty string handling
        [TestCase("123", "MTIz")] // byte array length equal to 4
        [TestCase("12345678901234567890", "MTIzNDU2Nzg5MDEyMzQ1Njc4OTA")] // longer string handling
        [Test]
        public void Convert(string str, string expected)
        {
            // Given, When, Then
            Assert.That(str.ToBase64Url(), Is.EqualTo(expected) );
            Assert.That(str.ToBase64Url().FromBase64Url(), Is.EqualTo(str));

            // Given, When, Then
            Assert.That(expected.FromBase64Url(), Is.EqualTo(str));
            Assert.That(expected.FromBase64Url().ToBase64Url(), Is.EqualTo(expected));
        }

        [TestCase(null)]
        public void NullHandling(string str)
        {
            // Given, When, Then
            Assert.Throws(Is.TypeOf<ArgumentNullException>()
                .And.Message.Contains("str"), () => str.ToBase64Url());
        }
    }