We present two Mixed-Integer Linear Programming (MILP) models for a complete microgrid planning problem which consider uncertainties in the main input data (hourly solar irradiance, wind speed and electricity demand). The first model adopts a Two-Stage Stochastic Integer Programming (2SSIP) formulation with discrete scenarios, whereas the second model adopts a Robust Optimization (RO) formulation with polyhedral uncertainty sets. The aim is to determine the optimal combination, capacities, and number of components to install in the microgrid considering long-term operations and uncertainty in the main input data. The 2SSIP model offers the possibility to obtain a planning solution using discrete scenarios sampled from appropriate probability distributions. The RO model gives a planning solution which is guaranteed to be feasible for any realization of input data within specified uncertainty sets. To show and compare the effectiveness of these models, we present a case study in which we apply the two models to plan a standalone microgrid in Singida, Tanzania. The proposed models can be applied for planning and detailed feasibility studies on generic microgrids with renewables, storage batteries and diesel generators.