No, reciprocity failure is different from film to film, so a light meter cannot know how to adjust for that. Some films don't need any adjustment up to a minute or longer, and some need adjustment after just a second.

Basically, you find the datasheet on the film you're using, and that will tell you what sort of correction it needs. If it requires 1 stop of correction, just keep your shutter open for twice as long, if it needs 2 stops, then it's 4 times as long, 3 stops, 8 times as long etc. You double the amount of exposure for each stop.

Generally I find that you can be pretty lax though, if you're doing long exposures, it's likely at night, and overexposure matters less, i.e. a black sky is a black sky, but during the day a blue sky will turn white with overexposure.

Trial and error is the order of the day really.