The paper deals with some combinations of conforming and nonconforming rectangular finite elements in order to obtain twosided bounds of eigenvalues, applied to second-order elliptic opertor. The aim is to use the lowest possible order finite elements. Namely, the combination of serendipity conforming and rotated bilinear nonconforming elements is considered in details. This work continues some recent researches of the authors concerning eigenvalue approximations. Computational aspects of the used algorithm are also discussed. Finally, results from numerical experiments are presented.