The largest databases in use today are so large that answering a query exactly can take minutes, hours, or even days. One way to address this problem is to make use of approximation algorithms. Previous work on online aggregation has considered how to give online estimates with everincreasing accuracy for aggregate functions over relational join and selection queries. However, no existing work is applicable to online estimation over subset-based SQL queries–those queries with a correlated subquery linked to an outer query via a NOT EXISTS, NOT IN, EXISTS, or IN clause (other queries such as EXCEPT and INTERSECT can also be seen as subset-based queries). In this paper we develop algorithms for online estimation over such queries, and consider the difficult problem of providing probabilistic accuracy guarantees at all times during query execution.