The COVID-19 pandemic has created urgent demand for timely data, leading to a surge in mobile phone surveys for tracking the impacts of and responses to the pandemic. Using data from national phone surveys implemented in Ethiopia, Malawi, Nigeria and Uganda during the pandemic and the pre-COVID-19 national face-to-face surveys that served as the sampling frames for the phone surveys, this paper documents selection the biases in individual-level analyses based on phone survey data. In most cases, individual-level data are available only for phone survey respondents, who we find are more likely to be household heads or their spouses and non-farm enterprise owners, and on average, are older and better educated vis-a-vis the general adult population. These differences are the result of uneven access to mobile phones in the population and the way that phone survey respondents are selected. To improve the representativeness of individual-level analysis using phone survey data, we recalibrate the phone survey sampling weights based on propensity score adjustments that are derived from a model of an individual's likelihood of being interviewed as a function of individual- and household-level attributes. We find that reweighting improves the representativeness of the estimates for phone survey respondents, moving them closer to those of the general adult population. This holds for both women and men and for a range of demographic, education, and labor market outcomes. However, reweighting increases the variance of the estimates and, in most cases, fails to overcome selection biases. This indicates limitations to deriving representative individual-level estimates from phone survey data. Obtaining reliable data on men and women through future phone surveys will require random selection of adult interviewees within sampled households.