Using model projections to study the emergence of observable climate signals presumes omniscient knowledge about the climate system. In reality, observational knowledge suffers from data quality and availability issues. Overlooking such deficiencies leads to misrepresentations of the time of emergence (ToE). We introduce a new definition of ToE that accounts for observational limitations (e.g., data gaps, gridding, changes in instrumentation, retrieval algorithms, etc), and show the potential for significant corrections to achieve the same statistical confidence as would be afforded by omniscient knowledge. We also show how our method can inform future observational needs and observing systems design.