We report the results of quasi-simultaneous two-filter optical monitoring of two high-energy peaked blazars, 1ES 1959+650 and 1ES 2344+514, to search for microvariability and short-term variability (STV). We carried out optical photometric monitoring of these sources in an alternating sequence of B and R passbands, and have 24 and 19 nights of new data for these two sources, respectively. No genuine microvariability (intranight variability) was detected in either of these sources. This non-detection of intranight variations is in agreement with the conclusions of previous studies that high-energy peaked BL Lacs are intrinsically less variable than low-energy peaked BL Lacs in the optical bands. We also report the results of STV studies for these two sources between 2009 July and 2010 August. Genuine STV is found for the source 1ES 1959+650 but not for 1ES 2344+514. We briefly discuss possible reasons for the difference between the intranight variability behaviour of high- and low-energy peaked blazars.