diff --git a/public/Get-DbaAgBackupHistory.ps1 b/public/Get-DbaAgBackupHistory.ps1
index 160868ca74b..ac2559d57ec 100644
--- a/public/Get-DbaAgBackupHistory.ps1
+++ b/public/Get-DbaAgBackupHistory.ps1
@@ -260,7 +260,9 @@ function Get-DbaAgBackupHistory {
             $replicaNames = ($server.AvailabilityGroups | Where-Object { $_.Name -in $AvailabilityGroup } ).AvailabilityReplicas.Name
             Write-Message -Level Verbose -Message "We have found these replicas: $replicaNames"
 
-            $serverList = $replicaNames
+            # With a single replica, Name returns a scalar string and indexing it with [0] below
+            # would yield its first character instead of the replica name, so force an array.
+            $serverList = @($replicaNames)
         }
 
         Write-Message -Level Verbose -Message "We have more than one server, so query them all and aggregate"
@@ -279,7 +281,7 @@ function Get-DbaAgBackupHistory {
 
         if ($Last) {
             Write-Message -Level Verbose -Message "Filtering Ag backups for Last"
-            $AgResults | Select-DbaBackupInformation -ServerName $AvailabilityGroup
+            $AgResults | Select-DbaBackupInformation -ServerName $AvailabilityGroup -EnableException:$EnableException
         } elseif ($LastFull) {
             Write-Message -Level Verbose -Message "Filtering Ag backups for LastFull"
             Foreach ($AgDb in ( $AgResults.Database | Select-Object -Unique)) {
diff --git a/tests/Get-DbaAgBackupHistory.Tests.ps1 b/tests/Get-DbaAgBackupHistory.Tests.ps1
index 878e4f2250c..2dfac8c996d 100644
--- a/tests/Get-DbaAgBackupHistory.Tests.ps1
+++ b/tests/Get-DbaAgBackupHistory.Tests.ps1
@@ -37,4 +37,119 @@ Describe $CommandName -Tag UnitTests {
     }
 }
 
-# No Integration Tests, because we don't have an availability group running in AppVeyor
\ No newline at end of file
+Describe $CommandName -Tag IntegrationTests {
+    BeforeAll {
+        # We want to run all commands in the BeforeAll block with EnableException to ensure that the test fails if the setup fails.
+        $PSDefaultParameterValues["*-Dba*:EnableException"] = $true
+
+        # For all the backups that we want to clean up after the test, we create a directory that we can delete at the end.
+        $backupPath = "$($TestConfig.Temp)\$CommandName-$(Get-Random)"
+        $null = New-Item -Path $backupPath -ItemType Directory
+
+        # To get availability group backup history we need an availability group and a database with backups.
+        # A single replica availability group with cluster type NONE is enough.
+        $agName = "dbatoolsci_agbackuphistory"
+        $agDbName = "dbatoolsci_agbhdb_$(Get-Random)"
+
+        $splatAg = @{
+            Primary      = $TestConfig.InstanceHadr
+            Name         = $agName
+            ClusterType  = "None"
+            FailoverMode = "Manual"
+            Certificate  = "dbatoolsci_AGCert"
+        }
+        $null = New-DbaAvailabilityGroup @splatAg
+
+        $null = New-DbaDatabase -SqlInstance $TestConfig.InstanceHadr -Name $agDbName
+        $splatBackup = @{
+            SqlInstance = $TestConfig.InstanceHadr
+            Database    = $agDbName
+            Path        = $backupPath
+        }
+        $null = Backup-DbaDatabase @splatBackup -Type Full -FilePath "agbh_full.bak"
+        $splatAddAgDatabase = @{
+            SqlInstance       = $TestConfig.InstanceHadr
+            AvailabilityGroup = $agName
+            Database          = $agDbName
+        }
+        $null = Add-DbaAgDatabase @splatAddAgDatabase
+        $null = Backup-DbaDatabase @splatBackup -Type Log -FilePath "agbh_log.trn"
+
+        # We want to run all commands outside of the BeforeAll block without EnableException to be able to test for specific warnings.
+        $PSDefaultParameterValues.Remove("*-Dba*:EnableException")
+    }
+
+    AfterAll {
+        # We want to run all commands in the AfterAll block with EnableException to ensure that the cleanup fails loudly.
+        $PSDefaultParameterValues["*-Dba*:EnableException"] = $true
+
+        # Cleanup all created objects.
+        $null = Remove-DbaAvailabilityGroup -SqlInstance $TestConfig.InstanceHadr -AvailabilityGroup $agName
+        $null = Get-DbaEndpoint -SqlInstance $TestConfig.InstanceHadr -Type DatabaseMirroring | Remove-DbaEndpoint
+        $null = Remove-DbaDatabase -SqlInstance $TestConfig.InstanceHadr -Database $agDbName
+
+        # Remove the backup directory.
+        Remove-Item -Path $backupPath -Recurse
+
+        $PSDefaultParameterValues.Remove("*-Dba*:EnableException")
+    }
+
+    Context "Gets the last backup chain of the availability group" {
+        BeforeAll {
+            $results = @(Get-DbaAgBackupHistory -SqlInstance $TestConfig.InstanceHadr -AvailabilityGroup $agName -Last)
+        }
+
+        # Always include this test to be sure that the command runs without warnings.
+        It "Does not warn" {
+            $WarnVar | Should -BeNullOrEmpty
+        }
+
+        It "Returns the full and the log backup tagged with the availability group name" {
+            $results.Type | Should -Contain "Full"
+            $results.Type | Should -Contain "Log"
+            $results.AvailabilityGroupName | Select-Object -Unique | Should -Be $agName
+        }
+    }
+
+    Context "Honors EnableException when no full backup anchors the chain #10621" {
+        BeforeAll {
+            $PSDefaultParameterValues["*-Dba*:EnableException"] = $true
+
+            # A history window that starts after the full backup and holds only a log backup, so the
+            # last-chain selection finds a log backup but no full backup to anchor it. We use -Since
+            # instead of deleting msdb history, because Backup-DbaDatabase refuses a log backup for a
+            # database whose msdb history holds no full backup. The sleeps keep the timestamp strictly
+            # between the existing backups and the new log backup.
+            Start-Sleep -Seconds 1
+            $sinceTime = Get-Date
+            Start-Sleep -Seconds 1
+            $null = Backup-DbaDatabase @splatBackup -Type Log -FilePath "agbh_log2.trn"
+
+            $PSDefaultParameterValues.Remove("*-Dba*:EnableException")
+        }
+
+        It "Throws with EnableException" {
+            $splatAgHistory = @{
+                SqlInstance       = $TestConfig.InstanceHadr
+                AvailabilityGroup = $agName
+                Last              = $true
+                Since             = $sinceTime
+                EnableException   = $true
+            }
+            { Get-DbaAgBackupHistory @splatAgHistory } | Should -Throw "*Fullname property not found*"
+        }
+
+        It "Still warns and returns nothing without EnableException" {
+            $splatAgHistory = @{
+                SqlInstance       = $TestConfig.InstanceHadr
+                AvailabilityGroup = $agName
+                Last              = $true
+                Since             = $sinceTime
+                WarningAction     = "SilentlyContinue"
+            }
+            $results = Get-DbaAgBackupHistory @splatAgHistory
+            $WarnVar | Should -BeLike "*Fullname property not found*"
+            $results | Should -BeNullOrEmpty
+        }
+    }
+}
\ No newline at end of file