Since the days of just walking into a place of business and handing someone a resume are long gone, what is the best way to follow up with an application? I know you can email but most HR departments will follow up with a generic email about not emailing them back. Unless you know someone, the chances of you getting an interview with a company are slim to none. Any suggestions?
Man, it's tough these days. When my wife and I relocated to this area (DMV area) back in 2014, I had a devil of a time job hunting. I have an earned doctorate, but those are a dime a dozen around here, so that didn't help me much. And, in reference to your OP, EVERYTHING is electronic. Most places didn't even provide an email or phone number for you to call. You just applied through their online system and just hoped it actually made it through somewhere. Sometimes I'd get an automatic reply at least confirming my application was received. Sometimes not. Some places SPECIFICALLY instructed you not to email or call. So many places now just use programs to scan resumes for key words or phrases. Applicants may also be sorted based on responses to questions in the electronic application.
For federal jobs, listings are posted on USAJOBS. Each application runs you through a list of questions about qualifications/competencies, with responses from A - E, with A being "not qualified at all" and E being "expert." If you even want your application to simply make it past the initial screening stage, where unqualified applicants are screened out electronically, you have to answer "E" to EVERY question. Because that's everyone else is doing. I made the mistake of answering my questions honestly, either saying I had some experience with certain techniques or was proficient. But you have to say you're expert, otherwise, all the other people who are saying they're expert will have their resumes advanced. Even if your application advances, it stands a slim shot of actually being viewed by a human being b/c resumes are scanned electronically. The trick here, which I also didn't know, is that you need to word your resume using EXACTLY the wording in the job listing. For you qualifications, you use the exact same words as the job duties described. It's all nuts.
So, all this to say, I experienced the same issues as you and, at least around here, there was really nothing to do about it. If I could have gotten through to anyone, I would have received, at most, a courtesy response. If there was an HR email address, there was usually a specific instruction not to email about job postings or applications. If you did email HR, you'd have gotten a form reply from some random HR person. The vast majority of places hiring professionals don't even allow you the opportunity to get in front of someone and make a good impression unless you get through all the electronic stuff.