Typical demands for magnetic field sensor applications are high dynamic magnetic field ranges, ambient temperature operation, small dimensions, necessary for high spatial resolution, and low energy consumption. In the case of sensors for biomagnetic sensing very high requirements in case of sensitivity and limit of detection (LOD) in the pT/Hz^1/2 to fT/Hz^1/2 range arise. Surface acoustic wave (SAW) sensors based on the delta E effect combine the advantages of small form factor, ambient temperature operation and high sensitivity. The SAW sensor consists of a piezoelectric quartz substrate, a silicon oxide layer and a magnetoelastic (Fe₉₀Co₁₀)₇₈Si₁₂B₁₀ layer, deposited on top of the oxide layer. Between interdigital transducers (IDTs) at the ports of the sensor, horizontal shear (Love) waves propagate. The oxide layer serves as a guiding layer. If an external magnetic field is applied, the magnetization alterations in the FeCoSiB layer are accompanied by changes of the shear modulus G and the wave propagation changes. The phase change of a transmitted signal serves as a measure of a magnetic field. Very low phase noise read out electronics is required to detect the phase changes. Heterodyne and homodyne electronic read out circuits are equivalent in performance while homodyne systems are advantages in terms of monolithic integration. The presented SAW sensors reach a high sensitivity with an LOD of 152 pT/Hz^1/2 at 10 Hz and 52 pT/Hz^1/2 at 100 Hz.