We establish estimation methods to determine co-jumps in multivariate high-frequency data with nonsynchronous observations and market microstructure noise. The ex-post quadratic covariation of the signal part, which is modeled by an Itˆo-semimartingale, is estimated with a locally adaptive spectral approach. Locally adaptive thresholding allows to disentangle the co-jump and continuous part in quadratic covariation. Our estimation procedure implicitly renders spot (co-)variance estimators. We derive a feasible stable limit theorem for a truncated spectral estimator of integrated covariance. A test for common jumps is obtained with a wild bootstrap strategy. We give an explicit guideline how to implement the method and test the algorithm in Monte Carlo simulations. An empirical application to intra-day tick-data demonstrates the practical value of the approach.