What’s your process for following up on unscheduled quotes?

One thing I’d add is that the wording of the follow-up matters just as much as the timing.  
A message that only says “just checking in” doesn’t give the customer much reason to reply. I think it works better to refer to the actual quote and give them one easy question or next step.  
Something as simple as asking whether they have any questions about the quote, or whether timing is the issue, makes the follow-up feel more useful and less pushy.