Viscoelasticity is an effect seen in a wide range of materials, and it affects the reliability of static measurements made using fiber Bragg grating (FBG)-based sensors, because the target structure, the adhesive used, or the fiber itself could be viscoelastic. The effect of viscoelasticity on FBG-based sensing has been comprehensively researched through theoretical analysis and simulation using a finite-element approach, and a further data processing method to reconstruct the graphical data has been developed. An integrated sensor package comprising an FBG-based sensor in a polymer host and manufactured by using three-dimensional (3D) printing was investigated and examined through tensile testing to validate the approach. The application of the 3D-printed FBG-based sensor package, coupled with the data process method, has been explored to monitor the height of a railway pantograph, a critical measurement requirement to monitor elongation, employing a method that can be used in the presence of electromagnetic interference. The results show that the effect of viscoelasticity can be effectively eliminated, and the graphical system response allows results that are sufficiently precise for field use to be generated.