Radar data enable us to estimate an asteroid's near-surface bulk density, thus providing a joint constraint on near-surface porosity and solid density. We investigate two different approaches to simplifying this joint constraint: estimating solid densities by assuming uniform porosities for all asteroids; and estimating porosities by assuming uniform mineralogy within each taxonomic class. Methods used to estimate asteroids' near-surface solid densities from radar data have not previously been calibrated via independent estimates. Recent spacecraft results on the chondritic nature of 433 Eros now permit such a check, and also support porosity estimation for S-class objects. We use radar albedos and polarization ratios estimated for 36 main-belt asteroids and nine near-Earth asteroids to estimate near-surface solid densities using two methods, one of which is similar to the uncalibrated algorithms used in previous studies, the other of which treats Eros as a calibrator. We also derive porosities for the same sample by assigning solid densities for each taxonomic class in advance. Density-estimation results obtained for Eros itself are consistent with the uncalibrated method being valid in the mean; those derived for the full sample imply that uncalibrated solid densities are, at most, a few tens of percent too large on average. However, some derived densities are extremely low, whereas most porosity estimates are physically plausible. We discuss the relative merits of these two approaches.