Here's how a local farm makes Elderflower Cordial (and I do to, from this recipe):

20-30 heads elderflower
Rind and juice of 2 lemons
1 kg sugar
30g tartaric or citric acid
1 Camden tablet

Put flowers in bowl/bucket with lemon and acid. Pour a litre of boiling water over the sugar and stir to dissolve. Add to the bowl with a Camden tablet. Leave for 24-36 hours (taste it to see if it's flowery enough) and then bottle or freeze. Makes about a litre and a half.

The boiling water helps kill natural yeasts on the blossoms, and the Camden tablet helps to prevent fermentation, so it should keep quite well, but freezing is probably safer if you want to keep it a long time.