The frequency response of ultrasonic detectors is commonly calibrated by finding their sensitivity to incident plane waves at discrete frequencies. For certain applications, such as the emerging field of optoacoustic tomography, it is the response to point sources emitting broadband spectra that needs to be found instead. Although these two distinct sensitivity characteristics are interchangeable in the case of a flat detector and a point source at infinity, it is not the case for detectors with size considerably larger than the acoustic wavelength of interest or those having a focused aperture. Such geometries, which are common in optoacoustics, require direct calibration of the acoustic detector using a point source placed in the relevant position. In this paper, we report on novel cross-validating optoacoustic methods for measuring the frequency response of wideband acoustic sensors. The approach developed does not require pre-calibrated hydrophones and therefore can be readily adopted in any existing optoacoustic measurement configuration. The methods are successfully confirmed experimentally by measuring the frequency response of a common piezoelectric detector having a cylindrically focused shape.