When you pitch an Op-Ed editor, you need to appreciate that they're driven by the news. At the New York Times, for example, the Op-Ed page receives 1,500 unsolicited pieces every week. They're busy! You may not get an instant response.
That said, you can't wait forever to hear back from an editor. Especially if your pitch is news sensitive, you need to let an editor know that you hope to hear from them within a short period of time—anywhere from 24 hours to two weeks, depending on the urgency of the piece (and the timeliness), and also depending on how much you'd like to publish in their paper.
But after a set amount of time—let's say two days for the sake of this lecture—if you haven't heard back, you'll need to email your editor and let them know that you'll be taking your work elsewhere. A polite way to say this is as follows: "Dear editor: I haven't heard back from you regarding my op-ed (see below). I'd still love to publish it in your paper, but as it's timely, if I don't hear back from you by the end of the day, I'll assume you've passed and will be submitting it elsewhere."
Note: It's important to send this sort of email before you actually submit a piece to a new venue. Most national outlets will not consider a piece if you have simultaneously submitted to multiple outlets.
If an editor responds to a query, you must always thank him or her—even if the response was "no thank you." Many people think a rejection is a bad thing. In fact, a rejection is the beginning of a relationship.
If you are strategic, charming, and intelligent in your response, you may be able to get the editor to explain to you why the piece you submitted didn't work for him/her. Perhaps the editor will tell you what his or her newspaper is looking for—or even, what piece he or she thinks you might be the perfect person to write.
If an editor invites you to submit further ideas, do so, and soon. Remember, editors need writers as much as we need them. Sooner or later, if you have good ideas and express them well—and can make a connection with an editor or two—the odds will fall in your favor. And once they do—that is, once your foot is in the door—the hard part is over. It's much easier to publish when you've got a published piece or two under your belt.
Follow Up: If the editor responds...
Thank your editor. Even if they said "no." Remember that "no" can be the beginning of a relationship that leads to "yes." If they published you, thank them not for showcasing you, but rather for giving space to the ideas and issues.
Follow Up: If there is no response...
Have a time limit. If your idea has a very short shelf life, you might give an editor a day or less to respond; if it's evergreen, a week or more. Then send a follow-up email to your editor saying that (of course) you'd still like to run your piece in their publication, but since the piece is timely, if you don't hear from them by the end of the day (week, whatever) you will assume they have passed, and you'll be submitting your op-ed elsewhere.
Note: Some newspapers will not consider your piece if you submit to multiple papers at the same time. If you do so, tell editors in your pitch.