How to check if a certain month has posts or not?

I’m working on my own theme. On a single page I want to show links to the archives of the previous and next months. However, if that month contains no posts, I don’t want to link to it. How can I check of a certain month has posts or not?

This code for example gives me a link to the previous month.

get_month_link(get_the_time('Y'), get_the_time('m')-1)

If that month contains no posts, the link redirects to a 404-page. I’d rather not show the link at all.