It's heartbreaking, I know, I've been in your situation and the crying and barking is so bad. However, each time you cave in and let them out, it reinforces the behavior. Start out by leaving the door open and feeding your dog in the crate. Any treats, put in the crate, so your dog has to go in to get them and starts associating the crate with good things instead of being contained. Put a few toys in so he has something to occupy himself with. To break the cycle you might want to get him an extra special treat that will keep him occupied for a while. I use those gravy basted chew bones. My dogs will chew on them forever. Then basically, start closing the door. If he cries, you have to let him cry. Don't look at him, talk to him, yell at him, just totally ignore him. When you do anything else you are giving him attention which is what he wants. It doesn't matter if it is negative attention. Once he stops whining and crying and barking for 5-10 minutes, go to the crate and let him out and praise him. As he stays quiet more often, you can extend the time necessary for him to be let out. He'll learn soon that he gets out of the crate when he is quiet. Like I mentioned, the first couple of days may be rough, but this method has worked for me even though for one dog I could only do it when my husband was gone (He couldn't stand to hear the crying). Every one of my dogs voluntarily enters their crates and stay for hours without a peep. Hope this method works for you as well as it has for me over the years. Ear plugs work well though I do understand that you can't let him bark for too long being in an apartment.
If he is doing it anytime he is put in the crate then it is unlikely to be separation anxiety. However, if it is only when you leave, this is called separation anxiety. First thing is to take your dog for a nice long walk before you leave, preferably 30 minutes or long. Make it a long, quick paced walk to tire your boy out.
Second is to use a low-key approach to leaving the house. Ignore your dog before you leave and after you come home for at least 5 minutes or more. If your house is like mine in the morning everyone is running around getting ready to leave. This has the dog in an excited mood and then suddenly he is alone. If this is the case, put him away from everyone, say in a bathroom until the frenzy is over.
Don't punish or shout at your dog when you come home and find he’s barked the whole time. When you do, you increase his stress level rather than reduce it.
You can provide him with small stimulating toys or toys that you can fill with treats.
Sometimes leaving a TV or radio on can help a dog with this problem as well. Also remember to not reward a dog's excitement to you with petting and affection or even eye contact. You want to show him nice calm praise when he is being calm.
You can also try practicing alone time by having him spend time away from you in a crate or other area away from you for short periods of time when you are home.
These should help his separation anxiety and boredom and help curb his barking. It will not be an overnight cure and will take work on your and your family’s part to be consistent in your interaction with him.
There are many other methods available to deal with barking such as citronella spray collar, shock bark collars (I personally am against shock collars) that will stop excessive barking. The citronella spray collars don't shock so that may be the alternative you are looking for.
Another option is medication, which is discussed on this site:
Hope this works for you.