Tail-sitters aim to combine the advantages of fixed-wing aircraft and rotorcraft but require a robust and fast stabilization strategy to perform vertical maneuvers and transitions to and from aerodynamic flight. The research conducted in this work explores different nonlinear control solutions for the problem of stabilizing a tail-sitter when hovering. For this purpose, the first controller is an existing strategy for tail-sitter control obtained from the literature, the second is an application of Nonlinear Dynamic Inversion (NDI), and the last one is its incremental version, INDI. These controllers were implemented and tuned in a simulation in order to stabilize a model of the tail-sitter, complemented by estimation methods that allow the feedback of the necessary variables. These estimators and controllers were then implemented in a microcontroller and validated in a Hardware-in-the-Loop (HITL) scenario with simple maneuvers in vertical flight. Lastly, the developed control solutions were used to stabilize the aircraft in experimental flight while being monitored by a motion capture system. The experimental results allow the validation of the model of the X-Vert and provide a comparison of the performance of the different control solutions, where the INDI presents itself as a robust control strategy with accurate tracking capabilities and less actuator demand.