Say you're trying to serialize a JSON API such as Google Maps where all the properties are lowercase and words are separated by underscores. But in order to keep your own code clean, you need to use camel casing...

UnderscoreContractResolver.cs

using System.Text.RegularExpressions;
using Newtonsoft.Json;
using Newtonsoft.Json.Serialization;

namespace Test
{
    public class FooTest
    {
        public void TestCustomResolver()
        {
            var settings = new JsonSerializerSettings
            {
                ContractResolver =
                    new UnderscoreContractResolver()
            };
    
            var bob = new { PropertyName = "asdf" };
            string json = JsonConvert.SerializeObject(bob, Formatting.Indented, settings);
    
            Assert.AreEqual("{\r\n  \"property_name\": \"asdf\"\r\n}", json);
        }
    }

    public class UnderscoreContractResolver : DefaultContractResolver
    {
        protected override string ResolvePropertyName(string propertyName)
        {
            return Regex.Replace(propertyName, "(?<=[a-z])[A-Z]", m => "_" + m).ToLower();
        }
    }
}