This dissertation thesis is a combination of three projects on magnetism and gravity studies of the Moon and a magnetism study of Mars, each with a heavy focus on uncertainty estimation. The goal of each chapter is to elucidate some portion of the thermal history of the Moon and Mars. Analysis of crustal magnetic fields can explain past dynamo behavior, which is tied to the amount of heat within a planet and how long it retains that heat. Elastic thickness, determined from correlations between gravity and topography, indicates the heat flux at the time of load emplacement and we can use the elastic thickness of a region to determine its formation age. The results from this thesis place constraints on the ancient dynamo behavior of the Moon and Mars (magnetism studies) and on the formation ages of portions of the farside of the Moon (gravity studies).Chapter 1 focuses on lunar crustal magnetic anomalies. The Moon no longer has an active global magnetic field, but evidence of an ancient field can be found in portions of the crust, which have been magnetized in the presence of intense fields thought to be generated by an extant dynamo. Quantifying the magnetization directions of these anomalies elucidates the behavior of the paleo-magnetic field by determining the magnetic paleopole (i.e., the orientation of the dipolar axis). Previously, distinguishing between paleopole locations was impossible because of their large uncertainties. Without distinguishing between paleopole locations, determining the history of the lunar dynamo is impossible. I propose an alternative method of estimating uncertainty using a Monte Carlo method to add synthetic noise to the best-fit modeled fields, which allows us to determine how easily perturbed the magnetization direction is in the presence of noise (i.e., uncorrelated anomalies). The new method more accurately describes the uncertainty of the inversion method and allows for better discernment of paleopole locations. I determined that the dipolar axis of the lunar dynamo must have been misaligned with the spin-axis at some point in lunar history, or that there were significant multipolar components to the magnetic field. Chapter 2 focuses on gravity and topography studies of the Moon. I use admittance analysis to determine the lunar elastic thickness and how it varies across the Moon. Elastic thickness allows us to determine the heat flux at the time of load emplacement, which in turn elucidates the thermal history of the Moon. Regions of low elastic thickness indicate high heating at the time of loading, and we can infer these locations formed earlier in lunar history than areas with higher elastic thicknesses. However, as in Chapter 1, variations in elastic thickness are meaningless without a clear estimate of uncertainty to distinguish between values. In this chapter, I describe how to determine elastic thickness using the spectral domain and the Markov chain Monte Carlo (MCMC) technique. Careful consideration is given to where these techniques are valid, including an analysis of the uncertainties from the MCMC technique using synthetic testing. I find that there are several locations on the Moon with low elastic thickness, implying these regions formed very early (<200 Myr) after the lunar magma ocean solidification. I also find one region with higher elastic thickness, which may be recording loading events as late as 3.5 Ga. Chapter 3 focuses on martian crustal magnetic anomalies. Like the Moon, Mars no longer has a global magnetic field, but there is evidence of a dynamo-generated field in the presence of widespread crustal magnetism. The issue of martian paleopole locations has plagued the magnetism community for two decades, many of the inferred paleopole locations do not correlate with each other, and several paleopole locations do not correlate with inferred paleo-spin axes calculated by other geophysical means. Additionally, there has not been a thorough paleopole analysis of crustal magnetic anomalies since the release of new magnetometer data from the NASA Mars Atmosphere and Volatile Evolution (MAVEN) mission. I use the methods described in Chapter 1 to determine the magnetic paleopole locations and uncertainties of ten martian crustal magnetic anomalies. I then use the Maximum Angular Deviation (MAD) technique to quantify the degree of clustering of our paleopole uncertainty ellipses and find significant clustering around a low latitude (45°N), which corresponds with a paleo-spin axis found through paleo-shoreline analysis (Perron et al., 2007). I show that the wide spread of other paleopole locations cannot be explained by a multipolar field or a hemispherical dynamo.