Saves a dictionary as key/value pairs. Importantly, it uses JsonConverters on the dictionary keys which the default JsonSerializer doesn't do.

CustomDictionaryConverter.cs

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using Newtonsoft.Json;

public class CustomDictionaryConverter : JsonConverter
{
    public override bool CanConvert(Type objectType)
    {
        return typeof(IDictionary).IsAssignableFrom(objectType) ||
               TypeImplementsGenericInterface(objectType, typeof(IDictionary<,>));
    }

    private static bool TypeImplementsGenericInterface(Type concreteType, Type interfaceType)
    {
        return concreteType.GetInterfaces()
            .Any(x => x.IsGenericType && x.GetGenericTypeDefinition() == interfaceType);
    }

    public override object ReadJson(JsonReader reader, Type objectType, object existingValue, JsonSerializer serializer)
    {
        var dictionaryTypeArguments = objectType.GetGenericArguments();

        var keyValuePairType = typeof(KeyValuePair<,>).MakeGenericType(dictionaryTypeArguments[0], dictionaryTypeArguments[1]);
        var keyValuePairKeyPropertyInfo = keyValuePairType.GetProperty("Key");
        var keyValuePairValuePropertyInfo = keyValuePairType.GetProperty("Value");

        var keyValuePairListType = typeof(IList<>).MakeGenericType(keyValuePairType);
        var keyValuePairList = (IEnumerable) serializer.Deserialize(reader, keyValuePairListType);

        var dictionaryType =
            typeof(Dictionary<,>).MakeGenericType(dictionaryTypeArguments[0], dictionaryTypeArguments[1]);
        var dictionaryAddMethodInfo = dictionaryType.GetMethod("Add", new []{ dictionaryTypeArguments[0], dictionaryTypeArguments[1] });
        var dictionary = Activator.CreateInstance(dictionaryType);

        foreach (var pair in keyValuePairList)
        {
            var key = keyValuePairKeyPropertyInfo.GetValue(pair, null);
            var value = keyValuePairValuePropertyInfo.GetValue(pair, null);
            dictionaryAddMethodInfo.Invoke(dictionary, new [] { key, value });
        }

        return dictionary;
    }

    // write the dictionary as key/value pairs
    public override void WriteJson(JsonWriter writer, object value, JsonSerializer serializer)
    {
        var type = value.GetType();
        var keys = (IEnumerable) type.GetProperty("Keys").GetValue(value, null);
        var values = (IEnumerable) type.GetProperty("Values").GetValue(value, null);
        var valueEnumerator = values.GetEnumerator();

        writer.WriteStartArray();
        foreach (var key in keys)
        {
            valueEnumerator.MoveNext();

            writer.WriteStartObject();
            writer.WritePropertyName("key");
            serializer.Serialize(writer, key);
            writer.WritePropertyName("value");
            serializer.Serialize(writer, valueEnumerator.Current);
            writer.WriteEndObject();
        }
        writer.WriteEndArray();
    }
}