You put the non-breaking space in the caption. Then the cross-reference field will update to include the non-breaking space where it needs to be.

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Andrew Lockton
Chrysalis Design, Melbourne Australia

Would I have to do this manually for every caption? In publishing in general, would most people just let "Figure" and the figure number separate onto different lines in this situation? I figured it was the same as keeping numbers and their units (e.g. 5 cm) on the same line but maybe it's not.