I had this problem as far as I remember and honestly I don't know why didn't MS add this feature (NH can do it like since always..).
Any ways, what I usually did is use const strings classes like:
public static class MyEnum
{
    public const string Foo = "Foo";
    public const string Bar = "Bar";
}
public class Client
{
    public string MyVal { get; set; }
    public Client()
    {
        MyVal = MyEnum.Bar;
    }
}
Cons - as simple as can be.
Downsides - you loose type checking (though it could be enforced programmatically).
So this time I tried to think of something more ambitious. So I took the concept described by Brian (which has some downsides when e.g. a given enum is used widely across the domain). And well.. I got the following working:
A base component class to store the values:
[ComplexType]
public class DbEnum<TEnum>
{
    public string _ { get; set; }
    public DbEnum()
    {
        _ = default(TEnum).ToString();
    }
    protected DbEnum(TEnum value)
    {
        _ = value.ToString();
    }
    public TEnum ToEnum()
    {
        return _.ToEnum<TEnum>();
    }
    public static implicit operator DbEnum<TEnum>(TEnum value)
    {
        return new DbEnum<TEnum>(value);
    }
    public static implicit operator TEnum(DbEnum<TEnum> value)
    {
        return value.ToEnum();
    }
}
... which would be basically sufficient.. except EF doesn't support generic types...
This means for every enum you have to have something like...
public enum PrivacyLevel
{
    Public,
    Friends,
    Private
}
public class PrivacyLevelEnum : DbEnum<PrivacyLevel>
{
    public PrivacyLevelEnum() : this(default (PrivacyLevel))
    {      
    }
    public PrivacyLevelEnum(PrivacyLevel value) : base(value)
    {
    }
    public static implicit operator PrivacyLevelEnum(PrivacyLevel value)
    {
        return new PrivacyLevelEnum(value);
    }
    public static implicit operator PrivacyLevel(PrivacyLevelEnum value)
    {
        return value.ToEnum();
    }
}
Which gives you some boiler-plate that could be easily generated e.g. using T4 templates. 
Which finally ends you up with using:
public class CalendarEntry : Entity
{
    public virtual PrivacyLevelEnum PrivacyLevel { get; set; } = new PrivacyLevelEnum();
}
But since you have implicit conversion in place, class declarations are the only ones to be aware of the helper types.