Proxy climate records are an invaluable source of information about the earth’s climate prior to the instrumental record. The temporal- and spatial-coverage of records continues to increase, however, these records of past climate are associated with significant uncertainties due to non-climate processes that influence the recorded and measured proxy values. Generally, these uncertainties are timescale-dependent and correlated in time. Accounting for structure in the errors is essential to providing realistic error estimates for smoothed or stacked records, detection of anomalies and identifying trends, but this structure is seldom accounted for. In the first of these companion articles we outlined a theoretical framework for handling proxy uncertainties by deriving the power spectrum of proxy error components from which it is possible to obtain timescale-dependent error estimates. Here in part II, we demonstrate the practical application of this theoretical framework using the example of marine sediment cores. We consider how to obtain estimates for the required parameters and give examples of the application of this approach for typical marine sediment proxy records. Our new approach of estimating and providing timescale-dependent proxy errors overcomes the limitations of simplistic single value error estimates. We aim to provide the conceptual basis for a more quantitative use of paleo-records for applications such as model-data comparison, regional and global synthesis of past climate states and data assimilation.