It's generally not free (and not that cheap) on cheaper fares.

Here's what AA ONN0NMN1 roundtrip coach fares (cheapest available) on LHR-SJO cost on a roundtrip basis. This has an overnight in MIA, but connection is less than 24 hours so it is not a stopover. Using SJO as an example here. Other Central American cities will likely be similar or identical (checked PTY and fare rules/stopover fees are the same).




Here's the stopover fees on ONN0NMN1 LHR-SJO fares if you want to have a connection that is longer than 24 hours.




Many cheap US-EU fares don't allow any stopovers at all and you will need to upfare to higher fares to get ones that have a stopover allowance. Here's stopover allowance for AA roundtrip QKX7F1B4 LHR-JFK fares.



Ultimately, it can often be cheaper to just book roundtrip fares on separate tickets if you want a connection longer than 24 hours. Rather than upfaring to something with a stopover allowance and paying the stopover fees.