This

CopyOptional.of(myMap.getOrDefault(myKey, null));

or really

CopyOptional.of(null);

would've failed with a NullPointerException. As the javadoc states

Throws:
NullPointerException - if value is null

Optional#ofNullable exists when you don't know if the value you're passing to it is null or not:

Parameters:
value - the possibly-null value to describe

And since Map#get(Object) already returns null when there is no entry for the given key

Returns:
the value to which the specified key is mapped, or null if this map contains no mapping for the key

you don't need to use getOrDefault with a null value for the default. You can instead directly use

CopyOptional.ofNullable(myMap.get(myKey));

You can create an optional based on a nullable value from other optionals:

public Optional<User> getUser(String id) {
    return Optional.ofNullable(
        cache.getUser(id).orElseGet(
            () -> repository.getUser(id).orElse(null)
        )
    );
}

But your current solution is clearly more readable.

For me the answer of @Dane White is OK, first I did not like using Runnable but I could not find any alternatives.

Here another implementation I preferred more:

Copypublic class OptionalConsumer<T> {
    private Optional<T> optional;

    private OptionalConsumer(Optional<T> optional) {
        this.optional = optional;
    }

    public static <T> OptionalConsumer<T> of(Optional<T> optional) {
        return new OptionalConsumer<>(optional);
    }

    public OptionalConsumer<T> ifPresent(Consumer<T> c) {
        optional.ifPresent(c);
        return this;
    }

    public OptionalConsumer<T> ifNotPresent(Runnable r) {
        if (!optional.isPresent()) {
            r.run();
        }
        return this;
    }
}

Then:

CopyOptional<Any> o = Optional.of(...);
OptionalConsumer.of(o).ifPresent(s -> System.out.println("isPresent " + s))
                .ifNotPresent(() -> System.out.println("! isPresent"));

Update 1:

the above solution for the traditional way of development when you have the value and want to process it but what if I want to define the functionality and the execution will be then, check below enhancement;

Copypublic class OptionalConsumer<T> implements Consumer<Optional<T>> {
private final Consumer<T> c;
private final Runnable r;

public OptionalConsumer(Consumer<T> c, Runnable r) {
    super();
    this.c = c;
    this.r = r;
}

public static <T> OptionalConsumer<T> of(Consumer<T> c, Runnable r) {
    return new OptionalConsumer(c, r);
}

@Override
public void accept(Optional<T> t) {
    if (t.isPresent()) {
        c.accept(t.get());
    }
    else {
        r.run();
    }
}

Then could be used as:

CopyConsumer<Optional<Integer>> c = OptionalConsumer.of(
    System.out::println, 
    () -> System.out.println("Not fit")
);

IntStream.range(0, 100)
    .boxed()
    .map(i -> Optional.of(i)
    .filter(j -> j % 2 == 0))
    .forEach(c);

In this new code you have 3 things:

1. can define the functionality before the existing of an object easy.
2. not creating object reference for each Optional, only one, you have so less memory than less GC.
3. it is implementing consumer for better usage with other components.

By the way, now its name is more descriptive it is actually Consumer<Optional<?>>