The best source for refurb (and discounted) iPhone 13 deals in general is Back Market. This site not only has a wide range of stock at great prices but you'll also get one full year of warranty ...

The iPhone 13 models have the same prices as their predecessors ... One obvious solution to that problem is to buy a used iPhone. You can score much better bargains if you’re willing to buy ...

Apple has discontinued the iPhone 13 now, so you’ll need to buy elsewhere. For comparison purposes, these were Apple’s prices, as of summer 2024. The iPhone 13 mini has also been discontinued.