Yes. Make sure they (matchmaker) have results of course but let's just say there are people out there who you will match with just fine.
One thing that women have to be "okay" with if you are searching for a match who isn't wanting to have kids, is guys who are a little older but that depends on various factors. If you don't want to have children and you're say 28-35, you want to look for a guy in his fourties (minimum) but who still is youthful so that he, if you are not one to go for older guys, doesn't give off the older guy vibe. In other words, you want to feel like he will be able to keep up with your level of energy. Can you find a match in your age group? Sure. Is it unlikely....um...yeah. And if a matchmaker hears that you insist they must be in your age group, they already know you're an impossible match (or rather unlikely) esp when you attach "no kids" to that group.
One thing I found a lot while working there is that people were just unreasonable. They wanted a guy their age, with no kids, who didn't want kids,and they got even more specific that he has to look like xyz with xyz job. Don't get me wrong I worked for an upscale matchmaker so the clients were always well off or rich and very busy which is why they came to her because they weren't the type to go to clubs, and they wanted to meet the love of their lives. So that's a given, but when you're so specific, then know that you're looking for a small % of avail men and as a matchmaker....they're going to roll their eyes at your application and kim. That doesn't mean to accept guys with kids either but have a reasonable list of what you want and don't want...it shouldn't be a mile long.
Should you have standards? sure. Just be reasonable and assess the situation. For instance: Most guys in their 30's are going to want to have children. (NOTE I SAID most). Most guys in their 40's and on will be divided into the "have children", "Want to have children but were to busy building their empire", "are cray cray in their expectations of women which is why they've never married (for the ones who never married and not all never marrieds fall into this group but by this age there is some cases where natural selection comes into play lol: some are pigs, ridiculous in their expectations, or so picky that they deserve to be laughed out of the office)" and finally the "don't want to have children" group.
If they waited this long, they could likely want to just have a wife and travel, or want little ones, or already have them. Then if they "have them" is there joint custody, is ex wife across country and he gets them on Holidays? Are you okay with that? Would you prefer someone with older kids (well then you're looking at a guy in his mid fourties to late in a major city at the minimum)...and you'll find the kids in the 16-18 age group ready to go off to (or already in college). Or did he wait to have kids all together and doesn't want them? And btw your matchmaker should be detailed in their questions or else you don't have a good one.
If you're the "second wife" you will still have to deal with possible little ones who visit (and if you're not okay with that, you're going to want to make that specific but open up your "age" group to older men so that you are still in the running with finding lots of matches), and if so (that you're open to little ones visiting, you need to make sure ex wife isn't bat s&^t cray cray, or the guy you're dealing with (because let's face it, sometimes it's the guys fault they're divorced too). In divorces you want amicable situations, or people who just grew out of love ideally especially when kids are involved and NO animosity on either parts. How do you start to find out? See how he refers to his ex (is it through gritted teeth, does he say horrid things about her, etc ?) Later of course when things are serious you'll want to meet the ex especially if there is talk of marriage.
I don't think I'll be set up with any dates though since I have reservations about wanting to have children and it seems like her clients for the most part want children. 
saw my mention. I'm not a matchmaker but I worked along side a hugely prominent one in the industry as her assistant. I thought of it as a "side job" to support my career as an artist but worked it full time and learned a TON there. So much so that you have to sign a non compete clause (for distance and a certain time where you can't open a competing business), etc because frankly I could start my own business with what I know, but it's just not for me (the field). I love the arts and that'swhere my heart lies. However I use it for the "good" of friends 
