We are going to talk about a two-dimensional model in statistical mechanics, the double-dimer model, which is simply a straightforward generalization of the dimer model. The latter is well-known in both physics and mathematics because of its particular features and substantial relations to many contexts, known in combinatorics as a perfect-matching problem. Here the emphasis is on the critical behavior of the loop ensembles of the double-dimer model, conjectured to converge to the level sets of the Gaussian free field and Schramm-Loewnerevolution or conformal loop ensembles with parameter 4. We use the Grassmannian representation of the dimer model to compute some loop-related observables in rectangular domains on the square lattice. The asymptotic behavior of the results in the continuum turns out to be consistent with previously known ones or with the aforementioned conjecture.