In this study, we consider risk-averse orienteering problems with stochastic travel times or stochastic rewards. In risk-neutral orienteering problems, the objective is generally to maximize the expected total reward of visited nodes. However, due to uncertain travel times or uncertain rewards, the dispersion in total reward collected may be large, which necessitates an approach that minimizes the dispersion (risk) in addition to maximizing the expected total reward. To handle this, for the orienteering problems with stochastic travel times or stochastic rewards, we suggest two different formulations with an objective of coherent measures of risk. For both problems, we conduct an experimental study using two different coherent measures of risk, which have been extensively used in the literature, and compare the results. The computational results show that, in both models suggested and under both risk measures used, the decision maker is able to obtain a tour with expected total reward being close to the expected total reward of risk-neutral solution, however with a significant decrease in the standard deviation of total reward.