Heriot is believed to have had at least four children by his first wife, including two sons who may have been drowned at sea, although the exact details of their death are unknown. He had no other legitimate children – his second marriage was childless – but in his will left money to provide for two natural daughters Elizabeth Band (born 1613) then aged ten and Margaret Scott (born 1619) then aged four. There were additional bequests to his stepmother and his half-siblings, as well as his nieces and nephews. However, the residue of the estate, some £23,625, was left to the city of Edinburgh, to establish a hospital for the free education of the "puir, faitherless bairns" of deceased Edinburgh burgesses.