In the context of the anomalous magnetic moment of the muon, the hadronic contribution plays a crucial role, especially given its large contribution to the final error. Currently, lattice QCD simulations are in disagreement with dispersive calculations based on \(e^+e^-\) hadronic cross sections. The new MUonE experiment intends to shed light on this situation extracting the hadronic contribution to the running of the electromagnetic coupling in the space-like region, \(\Delta\alpha_{\mathrm{had}}(t)\), from elastic \(e\mu\) scattering. Still, due to the limited kinematic range that can be covered by the experiment, a powerful method must be devised to accurately extract the desired hadronic contribution from a new experiment of this type. In this work, we show how Padé and D-Log Padé approximants profiting from the analyticity of the correlator governing the hadronic contribution can be a powerful tool in reaching the required precision.