You can try getting a new, bigger cage and placing them both in together. They will call out to each other as they are away from each other.
There is no guarantee that this will work though I am afraid.
If you choose to rehome one then you will have to spend as much time as possible with your budgie to help her get over the loss of her budgie friend.
You could try getting another male budgie perhaps I hope it all works out for you.