I wrote simple console application (based on "HOW TO: Upgrade a version 3.x database file to SQL Server Compact 4.0") to upgrade (convert) CE databases with previous verions to SQL Server Compact 4.0 There is the code: or you can download whole project of the tool.

/// Program.cs
using System;
using System.Data.SqlServerCe;

namespace CEUpdate
{
    class Program
    {
        static void Main(string[] args)
        {
            Console.Write(@"Source DB (*.sdf file Ex.: C:\Database.sdf): ");
            string sourceDB = Console.ReadLine().Trim();
            Console.Write("Password (If DB is password protected, otherwise hit Enter): ");
            string password = Console.ReadLine().Trim();
            Console.Write(@"Destination DB (*.sdf file Ex.: C:\temp.sdf): ");
            string destinationDB = Console.ReadLine().Trim();
            if (string.IsNullOrEmpty(sourceDB))
            {
                Console.WriteLine("Error: source DB can't be empty.");
                Console.Write("Press any key to exit...");
                Console.ReadKey();
            }
            else
                if (string.IsNullOrEmpty(destinationDB))
                {
                    Console.WriteLine("Error: destination DB can't be empty.");
                    Console.Write("Press any key to exit...");
                    Console.ReadKey();
                }
                else
                    if (sourceDB.Equals(destinationDB, StringComparison.CurrentCultureIgnoreCase))
                    {
                        Console.WriteLine("Error: destination and source can't be the same.");
                        Console.Write("Press any key to exit...");
                        Console.ReadKey();
                    }
                    else
                    {
                        string connection = "Data Source=\"" + sourceDB + "\"";
                        if (!string.IsNullOrEmpty(password))
                            connection += ";Password=" + password;
                        using (var engine = new SqlCeEngine(connection))
                        {
                            engine.EnsureVersion40(sourceDB, destinationDB);
                        }
                        Console.Write("Done! \nPress any key to exit...");
                        Console.ReadKey();
                    }
        }
    }
}

/// SqlCeUpgrade.cs
using System;
using System.Collections.Generic;
using System.IO;
using System.Data.SqlServerCe;

  public static class SqlCeUpgrade
  {
    public static void EnsureVersion40(this SqlCeEngine engine, string source, string destination)
    {
      SQLCEVersion fileversion = DetermineVersion(source);
      if (fileversion == SQLCEVersion.SQLCE20)
        throw new ApplicationException("Unable to upgrade from 2.0 to 4.0");

      if (SQLCEVersion.SQLCE40 > fileversion)
      {
          engine.Upgrade(String.Format("Data Source=\"{0}\"", destination));
      }
    }
    private enum SQLCEVersion
    {
      SQLCE20 = 0,
      SQLCE30 = 1,
      SQLCE35 = 2,
      SQLCE40 = 3
    }
    private static SQLCEVersion DetermineVersion(string filename)
    {
      var versionDictionary = new Dictionary<int, SQLCEVersion> 
      { 
        { 0x73616261, SQLCEVersion.SQLCE20}, 
        { 0x002dd714, SQLCEVersion.SQLCE30},
        { 0x00357b9d, SQLCEVersion.SQLCE35},
        { 0x003d0900, SQLCEVersion.SQLCE40}
      };
      int versionLONGWORD = 0;
      try
      {
        using (var fs = new FileStream(filename, FileMode.Open))
        {
          fs.Seek(16, SeekOrigin.Begin);
          using (BinaryReader reader = new BinaryReader(fs))
          {
            versionLONGWORD = reader.ReadInt32();
          }
        }
      }
      catch
      {
        throw;
      }
      if (versionDictionary.ContainsKey(versionLONGWORD))
      {
        return versionDictionary[versionLONGWORD];
      }
      else
      {
        throw new ApplicationException("Unable to determine database file version");
      }
    }
  }

Sources: