The life of plasmids is a constant battle against fluctuations: failing to correct copy number fluctuations can increase the plasmid loss rate by many orders of magnitude, as can a failure to more evenly divide the copies between daughters at cell division. Plasmids are therefore long-standing model systems for stochastic processes in cells, much thanks to the efforts of Kurt Nordström to whose memory this issue is dedicated. Here we analyze a range of experimental methods for measuring plasmid copy numbers in single cells, focusing on challenges, trade-offs, and necessary experimental controls. In particular we analyze published and unpublished strategies to infer copy numbers from expression of plasmid-encoded reporters, direct labeling of plasmids with fluorescent probes or DNA binding proteins fused to fluorescent reporters, PCR based methods applied to single cell lysates, and plasmid-specific replication arrest. We conclude that no method currently exists to measure plasmid copy numbers in single cells, and that most methods are overwhelmed by various types of experimental noise. We also discuss how accurate methods can be developed.