Whereas materials with intrinsic magnetoelectric (ME) effects have not yet made inroads in technology, the measurement of their tensor characteristics has become a precious tool for magnetic point group determination. Therefore, it is worthwhile to consider different measurement techniques. In particular techniques for determining the linear and bilinear ME effects will be discussed, essentially the quasi-static and dynamic magnetic field-induced methods will be evaluated. The measurement and application of ME “butterfly” loops for determining (weak) ferromagnetism and internal bias fields will be described. For the bilinear ME effect (with invariant EHH) a particularly sensitive measurement method with amplification effect will be highlighted, permitting, e.g., to detect subtle magnetic phase transitions. At least for the linear ME effect, we will stress that in the future only a dimensionless quantity should be used which is valid in all systems of units. Finally, the linear ME effect of TbPO4 crystals is reexamined because in a former publication it was not clear which system of units was effectively used (“rationalized” or “not rationalized” Gaussian system of units). Effectively, this crystal has the largest linear ME effect known. At T = 1.50 K, in SI units: αxy or αyx = 730 ps/m, i.e., 0.220 in “not rationalized” Gaussian system of units.