I ran a web design company for 5 years and having late payment terms in the contract was essential. When payment was late I'd typically write something like:

I ran a web design company for 5 years and having late payment terms in the contract was essential. When payment was late I'd typically write something like: "Thanks again for a fun project, the team really enjoyed working on it. I did notice that Invoice XXX was due on XX/XX. If you could let me know when it's in the mail, I'd greatly appreciate it. Thanks again and looking forward to collaborating again soon." I felt like it was important to bookend the request for money with two positive reinforcement statements to keep the tone predominantly friendly. If still no payment, then I'd send: "I want to quickly follow up on Invoice XXX. There's a late fee of $XX scheduled to go out on XX/XX. If you could kindly let me know that payment is in the mail before this Friday, I'll make sure the late fee gets cancelled." I felt like this respected their time and drove home the point that this issue wasn't going to be ignored on my end. I think it also sounded like I was on their side and wanting to help them which is key because once friendly discourse breaks down, it becomes infinitely more difficult. Another clause that was helpful was that ownership transferred when payment was made. So, in essence they were illegally using our creative work if it went live and they didn't pay. If the above didn't work, then a reminder of this usually did the trick. In the end, if it's more pain than it's worth, just let them go. If they're a good client, then collection is just an unfortunate necessity in service work unless you can setup a retainer which is nice, but you'll still have clients that want work done before their next retainer payment comes in. If you have more questions, I'm happy to chat. Email and website in my profile.