A quiet quote is not always a no. People get busy. The person who asked needs to speak to someone else. Your email landed under something else. It's also not always a yes that they're simply late to say. You won't know unless you ask, and asking is the bit that often doesn't happen, because it feels like pestering.
Don't leave the follow-up to memory
When you send the quote, note a day to follow up if you've heard nothing. Put it in the diary, or on the quote itself if your tool allows it. Two or three working days is enough for many small jobs; longer if you know they need to talk it over. The point is that the date is chosen while the job is still warm, not invented a fortnight later in a guilty rush.
Write a short check-in once, and reuse it. It can be almost nothing: you're just checking they got the quote, you're happy to talk it through, and they can say if the job has gone elsewhere. Civil, brief, and easy to answer. Save it next to your quote template so you aren't composing a new one each time, and tone-checking it while you feel ignored.
Follow up from the same thread or the same tool you used to send the quote, so they can see the original without hunting. If they then reply with a question, answer that and, if you need to, note a new day to close the loop.
A second follow-up, a little later, is reasonable for bigger jobs. After that, a lot of people let it rest. You can always keep the quote somewhere you can find it, in case they come back in a month. What you want to avoid is a long tail of half-remembered quotes, none of which has had a definite last word.
None of this is pushy if the wording is decent and the timing is fair. It's closer to good manners: you offered something, and you're checking it arrived.
We'd flag the silence, and draft the next note
We'd watch for quotes with no response and draft the follow-up, so nothing is sent without your say-so. You'd approve the wording first, and you can have different wording for a first check-in and a later one. The setup would sit in the quoting or bookkeeping tool you already use, or in one you choose, and it would be shaped to how you already send work out, not copied from someone else's pipeline.
You'd still decide when a job is truly dead, and you'd still handle the replies that need a human. The aim is that a quiet quote can't disappear just because the week got busy.
As with the rest of what we set up, the account is yours. You pay the software bill. We charge for the work. If we part company, the quotes and the follow-up wording stay in your system, and they keep working.
A follow-up won't win every quiet job. It will mean the ones that were only waiting for a nudge don't slip away, and that you spend less of the week wondering whether you should have said something.