Bring water and sugar to a boil over medium heat until sugar dissolves, 5 to 7 minutes. Remove from heat and let simple syrup cool.
Wash and slice clementine and lemon and place in a sealable glass jar along with elderflower and citric acid powder. Pour in cooled simple syrup, seal, and shake. Store in refrigerator for a minimum of 24 hours (and up to 72 hours, if stronger flavor is desired).
Strain cordial through cheesecloth into desired container, pressing down to extract all the liquid. Store in a sealed glass container in refrigerator for up to 3 months.
