Prepare a boiling water bath canner and five half pint jars.
In a low, wide pan, combine the raspberries, honey, lemon zest, and lemon juice. Place over hight heat and bring to a boil.
Cook at an active boil for 20 to 30 minutes, stirring regularly, until the fruit thickens. This preserve is never going to be as thick as jam made with pectin, but it should develop a soft set.
When the fruit has thickened to your liking, remove the pan from the heat.
Funnel preserves into prepared jars. Wipe rims, apply lids and rings, and process in a boiling water bath for 10 minutes.
When time is up, remove jars from canner and set them on a wooden cutting board or folded kitchen towel to cool.
Once they are cool enough to handle, test lids to ensure that jars have sealed. The lids will be concave and will be firm when pressed if seals are good.
Sealed jars are shelf stable up to one year. Any unsealed jars should be refrigerated and used promptly.