Enterobacterales with carbapenemase-independent resistance to carbapenems are sometimes being selected during therapy and, on rare occasions, cause outbreaks. Most have extended-spectrum or AmpC β-lactamases together with changes to permeability or penicillin-binding proteins (PBPs). Newer β-lactam-β-lactamase inhibitor combinations may present useful options for infections due to these organisms. Accordingly, we used CLSI/EUCAST broth-microdilution to measure MICs of ceftazidime/avibactam and aztreonam/avibactam for 51 carbapenemase/negative Enterobacterales with resistance or reduced susceptibility to carbapenems and undertook genomic sequencing of the least-susceptible organisms. MICs of the two avibactam combinations MICs cross-correlated closely, but with fewer MICs (2/51 versus 10/51) exceeding 8+4 mg/L in the case of ceftazidime/avibactam. Raised MICs for Escherichia coli were associated PBP3 inserts together with CMY-42 β-lactamase; correlates among Enterobacter cloacae complex isolates remain elusive, with AmpC and PBP3 sequences found to be sub-species specific. In the case of Klebsiella spp. no MICs exceeding 2 mg/L were seen for either combination. We conclude that these avibactam combinations have potential against Enterobacterales with carbapenemase-independent carbapenem resistance or reduced susceptibility, with ceftazidime/avibactam the more reliably active.