Workload consolidation is very attractive for cloud platforms due to several reasons including reduced infrastructure costs, lower energy consumption, and ease of management. Advances in virtualization hardware and software continue to improve resource isolation among consolidated workloads but a particular form of resource interference is yet to see a commercially widely adopted solution - the interference due to shared processor caches. Existing solutions for handling cache interference require new hardware features, extensive software changes, or reduce the achieved overall throughput. A crucial requirement for effective consolidation is to be able to predict the impact of cache interference among consolidated workloads. In this paper, we present a practical technique for predicting performance interference due to shared processor cache which works on current processor architectures and requires minimal software changes. While performance degradation can be empirically measured for a given placement of consolidated workloads, the number of possible placements grows exponentially with the number of workloads and actual measurement of degradation is thus not practical for every possible placement. Our technique predicts the degradation for any possible placement using only a linear number of measurements, and can be used to select the most efficient consolidation pattern, for required performance and resource constraints. An average prediction error of less than 4% is achieved across a wide variety of benchmark workloads, using XenVMMon Intel Core 2 Duo and Nehalem quad-core processor platforms. We also illustrate the usefulness of our prediction technique in realizing better workload placement decisions for given performance and resource cost objectives.