The radiofrequency (RF) safety constraints remain a major factor limiting the quality and speed of ultra-high field magnetic resonance imaging (UHF-MRI) and the use of parallel transmission (pTx) technology. Since the local Specific Absorption Rate (SAR) cannot be measured during an MRI examination, it is usually evaluated by off-line electromagnetic simulations using generic body models. To avoid potential local SAR underestimation due to deviations between actual and simulated MR examination scenario (such as differences in patient anatomy and in positioning, loading and coupling of the RF transmit array elements), the current most common practices are to include a safety factor around 2 and/or consider the worst-case peak local SAR value. Thus, the MRI exam can take more than double the actually required time for the same image quality. Software tools to perform on-line simulations using patient-specific body models are being developed but they still require a rather long on-line preparation time (to build the model, perform the simulations, and process the results). In this thesis, several important contributions and new concepts aimed at improving the performance of UHF-MRI systems are presented, with the most relevant being: the trigonometric maximization method to determine the actual worst-case local SAR without any overestimation in a few milliseconds (Chapter 2); the introduction of the 99.9% safe peak local SAR assessment concept to be used as an alternative to the worst-case local SAR (emerged from the extensive inter-subject local SAR variability analysis in Chapter 3 and underlying the conditional safety margin presented in Chapter 5); the first Artificial Intelligence (AI) approach for local SAR assessment (Chapter 4); and a Bayesian framework to more effectively address the inevitable residual error in the local SAR estimate and to identify potentially dangerous situations (Chapter 6). The use of these approaches reduced the mean local SAR overestimation error from over 100% to approximately 40%.