Interplanetary coronal mass ejections (ICMEs) are a significant feature of the heliospheric environment and the primary cause of adverse space weather at the Earth. ICME propagation and the evolution of ICME magnetic field structure during propagation are still not fully understood. We analyze the magnetic field structures of 18 ICME magnetic flux ropes observed by radially aligned spacecraft in the inner heliosphere. Similarity in the underlying flux rope structures is determined through the application of a simple technique that maps the magnetic field profile from one spacecraft to the other. In many cases, the flux ropes show very strong underlying similarities at the different spacecraft. The mapping technique reveals similarities that are not readily apparent in the unmapped data and is a useful tool when determining whether magnetic field time series observed at different spacecraft are associated with the same ICME. Lundquist fitting has been applied to the flux ropes, and the rope orientations have been determined; macroscale differences in the profiles at the aligned spacecraft may be ascribed to differences in flux rope orientation. Assuming that the same region of the ICME was observed by the aligned spacecraft in each case, the fitting indicates some weak tendency for the rope axes to reduce in inclination relative to the solar equatorial plane and to align with the solar east‐west direction with heliocentric distance. Plain Language Summary Coronal mass ejections (CMEs) are large eruptions of magnetic field and plasma from the Sun. When they arrive at the Earth, these eruptions can cause significant damage to ground and orbital infrastructure; forecasting this “space weather” impact of CMEs at the Earth remains a difficult task. The impact of individual CMEs is largely dependent on their magnetic field configurations, and an important aspect of space weather forecasting is understanding how CME field configuration changes with distance from the Sun. We have analyzed the signatures of 18 CMEs observed by pairs of lined‐up spacecraft and show that their basic magnetic field structures often display significant self‐similarities, that is, they do not often show significant reordering of field features with heliocentric distance. This similarity points to the general usefulness of placing spacecraft between the Sun and Earth to act as early‐warning space weather monitors. CME signatures observed at such monitors would likely be similar to the signatures subsequently arriving at the Earth and could be used to produce space weather forecasts with longer lead times. Key Points Eighteen interplanetary flux ropes observed by radially aligned spacecraft in the inner heliosphere have been examined Many of the flux ropes showed significant self‐similarities in magnetic field structure at the aligned spacecraft Macroscale differences in the magnetic field profiles are consistent with the flux ropes displaying different axis orientations